FOREARM SURFACE EMG SIGNALS RECOGNITION AND MUSCULOSKELETAL SYSTEM

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FOREARM SURFACE EMG SIGNALS RECOGNITION AND MUSCULOSKELETAL SYSTEM Powered By Docstoc
					   FOREARM SURFACE EMG SIGNALS RECOGNITION
     AND MUSCULOSKELETAL SYSTEM DYNAMICS
                 IDENTIFICATION
   USING INTELLIGENT COMPUTATIONAL METHODS



                             Dissertation
                 Zur Erlangung des akademischen Grades



                           Doktoringenieur
                             (Dr. –Ing.)
                                  Von
                        D. I. Abdelhafid Zeghbib
                           geb. am 20.04.63 in Algerien


 Genehmigt durch die Fakultät für Elektrotechnik und Informationstechnik
                                   der
OTTO-VON-GUERICKE UNIVERSITÄT MAGDEBURG, DEUSCHLAND


                                Gutachter:
               Univ.-Prof. Dr.-Ing.habil. Dr.h.c. Frank Palis
              Univ.-Prof. Dr.-Ing. habil. Heinz-Ulrich Seidel


                         Promotionskolloquium

                              am 07.12.2007
              To my mother my father my sisters and my brothers




I shall return again. I shall return
To laugh and love and watch with wonder-eyes
At golden noon the forest fires burn
Wafting their blue-black smoke to sapphire skies.
I shall return to loiter by streams
That bathe the brown blades of the bending grasses,
And realise once more my thousand dreams
Of waters rushing down the mountain passes.
                                                                                       by Claude McKay



Life is nothing but a big struggle, but just keep the faith and focus on your goals.
Don't let life beat you or you will be walking around like zombies.
Keep on pushing, keep on trying, life can be whatever you make it to be.
But life can also be a bowl of cherries with whip cream and apple pie.
I say this again; life is what you make of it.
You can achieve or conquer anything it throws at you,
you can't quit or give up, you have got to keep on working,
look higher some way, some how you are going to make it.

                                                                                         By David Cook
Acknowledgements
s —m deeply th—nkful to my —dvisorD €rofessor pr—nk €—lisD who initi—lly en™our—ged
me —nd introdu™ed me to this f—s™in—ting (eld of sntelligent ™omput—tion—l elgorithms
—s methods —nd ˜iomedi™—l engineering —s —ppli™—tionF s —m —lso th—nkful for his
™onst—nt support during this rese—r™hEperiodF s feel honored to h—ve h—d — ™h—n™e
to work with him in this rese—r™h for my ho™tor hegree —nd ˜e™—use of him to h—ve
re—™hed this degreeF ris l—rge experien™e —nd huge energy of work in rese—r™h h—ve
provided in me — ™ontinuous stimulus for my rese—r™hF
    s h—ve the ple—sure to th—nk —lso the p—rtners of our ™ommon proje™t @sym˜oli™
™ontrolling of —n —rti(™i—l h—nd using myoEele™tri™—l sign—lsD €rofF €ierre ‰ves qloE
renne™D €rofF pF fF yuezdou —nd hrF €—tri™k ren—'D did in ™ooper—tion ˜etween
Otto-von-Guericke …niversity w—gde˜urg qerm—nyD Max Planck snstitute w—gdeE
˜urg qerm—nyD sxƒeGs‚sƒe university Rennes-France —nd LIRIS v—˜or—tory in †erE
s—illes …niversity pr—n™eF
s should —lso mention th—nkful to Max Plank snstituteD in whi™h s h—ve h—d the possiE
˜ility to do —ll my me—surementsD through the help of my friend hrF „hom—s ƒ™h—uer
—nd his ingineer student ‚o˜ert ƒ—l˜ert who helped me —nd put the l—˜or—tory —t
my —v—il—˜ilityF
yf ™ourseD s —m —lso gr—teful to —ll person—ls of my dep—rtment for their supportD
spe™i—lly hrF ‚iemeu—stenD wsF ronymus —nd wsF uriegerD they were wonderful
people —nd their support m—kes —lso this work possi˜leF



qerm—ny                                                          e˜delh—(d egh˜i˜
w—r™h PUD PHHU




                                          i
ii
Zusammenfassung

Wie erreichen Menchen die beeindruckende Leistung während der Bewe-
gung?

    hiese hissert—tion fetr—™htet d—s ˜iologis™he ƒystem der fewegungD sie wird in
zwei „eilen d—rgestelltF sm ersten „eil steht die irkennung der gemessenen elekE
tromyogr—phis™hen ƒign—le der …nter—rmmuskeln im pokusD die den r—nd˜ewegunE
gen entspre™henF her zweite „eil ˜einh—ltet die fetr—™htung des wuskulosket—lE
ƒystemsD wel™hes den dyn—mis™hen unie˜eugewinkel unter isotonis™hen uontr—ktioE
nen d—rstelltF her d—˜ei gemessene ‡inkel zwis™hen dem ƒ™henkel und dem fein
zeigt d—s enspre™hverh—lten der elektris™hen ƒtimul—tion @piƒAF hieses †erf—hren ist
unter ƒystemidenti(k—tion ˜ek—nntF
h—s †erstehen der punktionen der mens™hli™hen fewegung ˜ildeten in der letzten
hek—de einen ƒ™hwerpunkt —uf dem qe˜iet der xeuromuskulären und ƒkelettären
ƒysteme innerh—l˜ der fiome™h—nikF uörper˜ewegungen stellen eine snter—ktion zwisE
™hen dem neuroEmuskulärem ƒteuersign—l und dem muskuloskelet—l hyn—miksystem
d—rF †iele ilemente des neuromuskuloskelet—l ƒystems wirken so —ufein—nder einD
d—ss eine rei˜ungslose und koordinierte fewegung ermögli™ht wirdF h—s skelett—rtige
ƒystemD ˜esteht —us uno™hen und deren †er˜indungen zu den wuskeln @ƒehnenAD die
d—s muskuloskelet—l ƒystem unterstützen E sie ü˜ertr—gen die notwendigen uontr—kE
tionen —uf d—s ƒkelett und re—lisieren d—mit die gewüns™hten fewegungenF sn dieser
hissert—tion konzentrieren wir uns zum iinen —uf die mens™hli™hen neuromus™ulären
ƒteuersign—le sowie deren ul—ssi(zierung und zum enderen —uf die sdenti(zierung der
muskuloskelet—l hyn—mikF hiese komplexen ƒysteme erfordern intelligente wodelleD
xeuron—l xetz und puzzy logi™D die dur™h künstli™he sntelligenz si™h —d—ptierenF
snform—tionenD in porm von xervenimpulsenD (gure ID w—ndern n—™h und von unserem

                                         iii
        iv



entr—lnervensystem @qehirnA entl—ng unseres ‚ü™kenm—rks und erl—u˜en unsD unE
sere freiwilligen fewegungen des uörpers zu koordinierenF ilektris™he smpulse des
qehirnsD die ü˜er die xervenzellen den wuskeln ü˜ermittelt werdenD verurs—™hen die
fewegungen @uontr—ktionenA dieser wuskelnF hiese wuskeln re—gierenD wenn sie die
elektris™hen ƒign—le des qehirns empf—ngenF hiese elektris™hen ƒign—le sind ü˜er die
wuskeln gemessen und sie sie sind —ls ile™tromyogr—phis™he ƒign—le @iwqA erk—nntF
hie mens™hli™he fewegung ist ein komplizierter €rozess und k—nn in die neuron—le


                                              Brain
                                              Command
                                               Spinal
                                               cord




                    EMG signal =                             Muscule
                    ∑ Motor Unit Potentials                  system
                                                    Muscle
                                                    fibers




pigure IX hie sllustr—tion des mens™hli™hen neuromuskulären ƒign—ls und des wuskeln
ƒystems —ls zwei uomponenten für hur™hführung der fewegung

ƒteuerungD die neuromuskulären ƒign—le und s™hlieÿli™h die wuskelkr—ft eingeteilt
werdenF sm ‚—hmen der vorliegenden hissert—tion stehen die zwei letzten uompoE
nente der fewegung im pokusX
IA irkennung der iwq ƒign—le @ul—ssi(zierungA und
PA hie sdenti(zierung der wuskuloskelet—lE dyn—mis™hen fel—stungF
h—s verurs—™hende †erhältnisD zwis™hen neuromus™ul—r iwq und mus™uloskelet—l
hyn—mikD wirdD in dieser hissert—tionD ni™ht ˜etr—™htetF tedes „eil gilt —ls —lleinF
h—s erste iel ist die irkennung des iwqD wel™hes die neuromuskulären ƒign—le
erkennt und kl—ssi(ziertF hieses neuromuskulär ƒign—l ˜esteht —us einzelnen wuskeE
l—ktionspotenti—len @w…e€sA von xervenF hie ƒumme der wuskelf—ser ektionspoE
tenti—le —ller wuskelf—sern k—nn mit rilfe der ilektroden gemessen werdenD die —uf
dem entspre™henden wuskel —ls ile™troEmyogr—phsign—l @iwqA gesetzt werdenF iin
entspre™hendes @ynlineEA €rogr—mm zur irkennung des iwqE ƒign—ls ist ˜ereits enE
twi™kelt wordenF
                                                                           v



h—s zweite iel dieser hissert—tion istD die muskuloskelet—l ƒtrukturdyn—mik zu idenE
ti(zierenD die für die fewegung des uörpers ver—ntwortli™h ist @feine und ermeAF
ƒol™he fewegungen können mit pun™tion—l ile™tri™—l ƒtimul—tion¤
                                   ¤                                 @piƒA produziert
werdenD sofern die hyn—mik zwis™hen der piƒ und der si™h d—r—us —˜leitenden feweE
gung ˜ek—nnt istF hieses ƒtudium k—nn —u™h für den ill˜ogen —ngewendet werdenF
iin ˜esseres †erständnis dieser zwei uomponenten der rum—n˜ewegungen @moveE
ment re—lis—tion dyn—mi™sAD wus™uloskelet—l v—st und xeuromuskulär ‚ekrutierungD
k—nn körper˜ehinderten €ersonen helfenD dur™h ‡iedergewinnung der verlorenen feE
wegungsfunktionen eine †er˜esserung ihrer ve˜ensqu—lität zu errei™henF ƒie unterE
stützt —u™h den ports™hritt der ‚eh—˜ilit—tion und ermögli™ht zudem eine ˜essere
iins™hätzung und ther—peutis™he feh—ndlung für körper˜ehinderte €ersonenF hiese
zwei uomponenten sind in dieser hissert—tion sep—r—t ˜eh—ndelt wordenF hie inE
twi™klung von te™hnis™hen †erf—hren für die irfors™hung des †erhältnisses zwis™hen
˜eiden uomponenten wird in der vorliegenden er˜eit von groÿem snteresse seinF wit
rilfe der ermittelten s™hw—™hen freiwilligen wuskel—ktivitäten ˜ei ƒ™hl—g—nf—llp—tienE
ten dur™h elektromyogr—phis™he ƒign—leD wel™he die elektris™hen ƒtimul—tionen @piƒA
steuernD k—nn dieses †erhältnis @der ˜eiden uomponentenA d—rgestellt werdenF hie
ƒteuerung der piƒEƒign—le wird den €—tienten helfenD eine korrekte fewegung der
erme undGoder der feine dur™hzuführenF hiese †erf—hren helfen d—s †erhältnis zwisE
™hen den me™h—nis™hen fewegungen und den iwqE iigens™h—ften zu ergründenF
hie —ktuelle „e™hnik erl—u˜t die te™hnis™he ennäherung —n die fiosign—lver—r˜eitung
sowie die sdenti(zierung sol™her komplizierter und dyn—mis™hen ƒysteme wie wuskelnD
die —ls qener—tor —ller fewegungen des mens™hli™hen uörpers zu ˜etr—™hten sindF
puzzy vogi™ ƒysteme und neuron—le xetze sind intelligente wethodenD die in dieser
hissert—tion für die vösung der sdenti(zierung und ul—ssi(zierung genutzt worden
sindF ƒie werden —ls ™omputerunterstütztes €ro˜lem d—rgestelltD um sie im t—gtägli™hen
komplexen ƒystem der fiomedizin —nzuwendenF
hiese ƒign—leD die von den wuskeln mittels y˜er)ä™henelektroden gemessen werE
denD erfordern weitere fere™hnungsmethoden für die irf—ssung @—quisitionAD en—lyseD
erlegung @de™ompositionAD und ul—ssi(k—tionF her we™k des ersten „eils ist die
sllustrierung der vers™hiedenen wethodologien und elgorithmen für —lle notwendigen
ƒ™hritteD die für die pingerE und r—nd˜ewegungen entspre™hend ihren iwqEƒign—len
zu erkennen sindF iin elgorithmus für die ul—ssi(k—tion dieser iwqEƒign—le konnte
˜ereits in früheren €u˜lik—tionen vorgestellt werdenF hie ul—ssi(k—tionserge˜nisse
        vi



dieses vorges™hl—genen elgorithmus werden mit —nderen ˜ek—nten fere™hnungsmethE
oden vergli™hen @puzzy logi™ und xeuron—le xetzAF hiese erste uomponente enthält
die intwi™klung —ller †erf—hren von iwqEƒign—len von der irf—ssung ˜is zur irkenE
nung ihrer entspre™henden r—ndE oder pinger˜ewegungen mittels ixtr—ktion der relE
ev—nten werkm—le und ihrer ul—ssi(k—tionF ‡eiterhin soll €—tienten mit —mputierten
qliedm—ÿen geholfen werdenF h—s ˜edeutetD d—ss die neuromuskulären ektivitätenD
˜eispielsweise seiner …nter—rmmuskelnD für die ƒteuerung der wyoE€rothese ˜enutzt
werdenF udem wird die ektivität seiner qehirnneurone entspre™hend der xeuronen
der …nter—rmsmuskeln d—uerh—ft —ngeregtF
hie zweite uomponente der ‚e—lisierung der rum—n˜ewegungenD d—s wuskuloskeleE
t—lsystemD ist von weiterem snteresseF hie hyn—mik dieses ƒystems ist komplexF h—E
her sollten wir n—™h einer e'ektiven wethode su™henD mit der diese komplizierte hyE
n—mik @wotorsystemA modelliert werden k—nnF w—them—tis™he wodellierungsmethoE
den @morphologis™he wodelleA können eine sol™he hyn—mik ni™ht mit qen—uigkeit @(E
delityA ˜es™hrei˜enF els weiterer feitr—g wird ein ry˜rid—lgorythmus vorges™hl—genD
um e'ektiver und s™hneller eine vösung @wuskuloskelet—lsystemA her˜eizuführenF hie
y˜ers™henkelmuskeln werden —ufgrund ihrer qrösse ˜etr—™htetF h—s erlei™htert die
gewüns™hten wuskeln zu stimulierenF hes ‡eiteren ermögli™ht die wuskel—usw—hl die
iindeutigkeit der ƒtimul—tionF enh—nd eing—ngs erzeugter elektris™her smpulse und
den d—r—us resultierenden ‡inkel zwis™hen dem unie und dem y˜ers™henkel können
die wodellp—r—meter des 4hy˜rid fuzzy identi(erEmodel4 ermittelt werdenF hie eisE
tungsfähigkeit des 4hy˜rid fuzzy identi(erEmodel4D d—s eine ni™ht line—re snputGyutputE
hyn—mik d—rstelltD hängt von der 4fuzzy p—rtition4 seines iing—ngE‚—umes —˜F @the
initi—lis—tion of premise fuzzy sets is —n import—nt issue in fuzzy modelingAF 4‚—pid
€rototyping4 wethode wird dur™h diesen vorges™hl—genen elgorithmus eingeführtD
um die veistung der sniti—lisierung der 4puzzy ƒets4 dur™hzuführenF hieses vorges™hl—E
genen ry˜rid—lgorithmus ˜esteht —us drei uomponentenX 4‚—pid €rototyping4 elgoE
rithmusD 4qr—dient hes™ent4 wethodD und 4ve—st ƒqu—res istim—tor4F elle diese drei
„eilen sind kom˜iniertD um diese wodellierungs—ufg—˜e dur™hzuführenF hes ‡eiteren
ermögli™ht die ƒteuerung der 4hum—n kneeEjoint movements4F
Abstract

How do humans achieve the remarkably impressive performance when they
move?

    „he spe™i(™ —im of this thesisD whi™h ™onsiders the ˜iologi™—l system 4hum—n
movement4D is presented in two p—rtsF „he (rst p—rt ™onsiders the re™ognition @™l—sE
si(™—tionA of me—sured ile™troEmyogr—phy @iwqA sign—ls of fore—rm mus™les ™orreE
sponding to h—nd movementsF „he se™ond p—rt tre—ts the mus™uloskelet—l systemD
whi™h is ™onsidered ˜y uneeEjoint dyn—mi™s under nonEisometri™ ™onditionsD in terms
of its me—sured —ngle ˜etween thigh —nd sh—nk —s response for pun™tion—l ile™tri™—l
ƒtimul—tion @FES A impulsesF „his pro™edure is known —s systemEidenti(™—tionF
…nderst—nding hum—n movement fun™tions is of — gre—t import—n™e in the dom—in of
neuromus™uloskelet—l systems —nd ˜iome™h—ni™sF ‡holeE˜ody movement is —™hieved
with help of the inter—™tion ˜etween the neuromus™ul—r ™ontrol sign—l —nd mus™uE
loskelet—l dyn—mi™s systemF w—ny elements of the neuromus™uloskelet—l system inE
ter—™t to en—˜le smooth —nd ™oordin—ted movementsF „he skelet—l systemD ™omposed
of ˜ones —nd joint ™onne™tions with mus™lesD whi™h ™omplete the mus™uloskelet—l sysE
temD —pply the ne™ess—ry driving for™es for movement re—lis—tionF sn this thesis we
will fo™us on hum—n xeuromus™ul—r ™ontrol sign—ls ™l—ssi(™—tion —nd wus™uloskelet—l
dyn—mi™s identi(™—tionF „hese ™omplex systems require mu™h knowledge ˜y le—rningF
ren™e —n improvement of the le—rning —˜ilityD using —rti(™i—l intelligent methodsD is
—lso ™overedF
„he inform—tionD in the form of nerve impulsesD (gure PD tr—vels to —nd from our
™entr—l nervous system @˜r—inA —long our spin—l ™ordD —llows us to ™oordin—te our volE
unt—ry movements of our ˜odyF fr—in ele™tri™—l impulsesD whi™h —re tr—nsmitted vi—
nerve ™ells to the mus™lesD ™—use the movement of these mus™lesF „hese mus™les reE
spond ˜y ™ontr—™ting when the ˜r—in9s ele™tri™—l sign—ls re—™h themF „hese ele™tri™—l

                                         vii
        viii



sign—ls ™—n ˜e me—sured over mus™les —nd they —re ™—lled ele™tromyogr—phy @iwqA
sign—lsF qener—tion of hum—n movement is — ™omplex pro™essD involving the following


                                               Brain
                                               Command
                                                Spinal
                                                cord




                     EMG signal =                             Muscule
                     ∑ Motor Unit Potentials                  system
                                                     Muscle
                                                     fibers




pigure PX sllustr—tion of hum—n neuromus™ul—r sign—l —nd mus™uloskelet—l system —s
two ™omponents of movement re—lis—tion

w—ysX neur—l ™omm—ndD neuromus™ul—r sign—ls —nd (n—lly mus™le for™eF „his thesis
™onsiders the two l—st ™omponents of movement re—lis—tionD whi™h —reX
IA iwq xeuromus™ul—r re™ruitment sign—ls re™ognition @™l—ssi(™—tionAD —nd
PA wus™uloskelet—l lo—ding dyn—mi™s identi(™—tionF
sn this thesis the ™—us—l rel—tionships ˜etween neuromus™ul—r iwq sign—ls —nd musE
™uloskelet—l dyn—mi™s will not ˜e ™onsideredF i—™h p—rt is ™onsidered —loneF
„he (rst go—lD is to re™ognise —nd ™l—ssify the iwq neuromus™ul—r sign—lF „his neuE
romus™ul—r sign—l represents the wotor …nit e™tion €otenti—ls @MUAPs A of nervesF
„he summ—tion of the mus™le (˜er —™tion potenti—ls from —ll mus™le (˜ers ™—n ˜e
me—sured with help of ele™trodes pl—™ed on the ™orresponding mus™le —s ele™tromyogE
r—phy @iwqA sign—lF en onEline elgorithm for this p—rt of iwq sign—ls re™ognition
is —lso developedF
„he se™ond go—l of this thesis is to identify mus™uloskelet—l stru™ture dyn—mi™sD whi™h
—™t —s —™tu—tors produ™ing the joint torques to drive the ˜ody @legs —nd —rmsAF ƒu™h
movements ™—n ˜e produ™ed using pun™tion—l ile™tri™—l ƒtimul—tions @FES AD if the
dyn—mi™s ˜etween FES —nd joint torques —re knownF elthough this p—rt of study
fo™uses on w—lkingD using qu—dri™eps mus™lesD the (ndings ™—n ˜e gener—lised to other
motor ™ontrol systems su™h —s el˜ow joint through ˜i™eps —nd tri™eps mus™lesF
e ˜etter underst—nding of these two ™omponents of movement re—lis—tion dyn—mi™s
                                                                             ix



@mus™uloskelet—l lo—d —nd neuromus™ul—r re™ruitmentA ™—n help dis—˜led persons in
reg—ining lost fun™tion —ndGor improving their —™tivity of d—ily living life —nd for —sE
sessing reh—˜ilit—tion progressF „hese two ™omponents h—ve ˜een studied in this thesis
sep—r—telyF heveloping te™hniques for investig—ting the rel—tionship ˜etween themD
in further workD will ˜e of gre—t import—n™eF ƒu™h rel—tionship ™—n ˜e illustr—ted
˜y using the re™ognition of dete™ted we—k volunt—ry mus™le —™tivityD ˜y postEstroke
su˜je™tsD through ele™tromyogr—phy sign—ls @iwqA to ™ontrol pun™tion—l ile™tri™—l
ƒtimul—tion @FES A impulsesD whi™h will support the p—tients to —™™omplish ™orre™t
leg or —rm movementsF „hese te™hniques help the investig—ting of the rel—tionship
˜etween the me™h—ni™s of movement —nd the ™h—r—™teristi™s of the iwq sign—ls
„he dom—in of engineers provides e0™ient te™hni™—l —ppro—™hes —nd tools for ˜ioE
sign—ls pro™essing —nd ™omplex dyn—mi™ systems identi(™—tion —s mus™leD whi™h is
the gener—tor of —ll hum—n ˜ody movementsF ƒoft ™omputing in™ludes ˜oth neur—l
networks @NN A —nd fuzzy logi™ @pvA systems represent intelligent —ppro—™hesD whi™h
—re used in this thesis for solving the identi(™—tion —nd ™l—ssi(™—tion pro˜lem of su™h
re—listi™ ™omplex systems in ˜iomedi™—l —re—F
„hese iwq sign—ls —™quired from mus™lesD through surf—™e ele™trodesD require —dE
v—n™ed ™omput—tion—l methods —s —™quisitionD —n—lysisD de™ompositionD —nd ™l—ssiE
(™—tionF „he purpose of this p—rt is to illustr—te the v—rious methodologies —nd
—lgorithms for —ll ne™ess—ry steps used to dis™rimin—te the di'erent movements of
(nger —nd h—nd gr—sps —™™ording to their ™orresponding iwq sign—lsF por the re™ogE
nition —nd ™l—ssi(™—tion of these iwq sign—lsD — fuzzyE™l—ssi(erEmodel —lgorithm is
proposed in this thesisF „his ™l—ssi(erEmodel —lgorithmD puzzy „rimmed we—n gl—ssiE
(er @FTMC A uses the trimmed me—n method —s tool for input sp—™eEset initi—lis—tionF
„he results of this —lgorithm —re ™omp—red with other known intelligent ™omput—E
tion—l methodsF „his (rst p—rt ™ont—ins the development of —ll pro™eduresD st—rting
from iwq sign—ls —™quisition till the re™ognition of their ™orresponding h—ndG(nger
movementsD using extr—™tion of relev—nt fe—tures —nd their ™l—ssi(™—tionF „he m—in
go—l of this (rst p—rt is to help the p—tient with the —mput—ted h—nd to keep the
neuromus™ul—r —™tivity of fore—rm mus™lesD whi™h will ˜e used to m—nipul—te — myoE
prosthesisD —nd to keep the virtu—l neur—l —™tivity of the ˜r—in rel—ted —lso to this
—™tivity of fore—rm9s motor unit potenti—ls F
„he se™ond ™omponent of movement re—lis—tion dyn—mi™sD whi™h is mus™uloskelet—l
dyn—mi™s h—s — gre—t import—n™eF „hese dyn—mi™s —re very ™omplexD hen™e we should
        x



look for —n e'e™tive method th—t ™—n model this ™omplex motor systemF w—them—tiE
™—l modelling methodsE˜—sed morphologi™—l models ™—nnot des™ri˜e with (delity su™h
™omplex dyn—mi™sF por this pro˜lem —n e'e™tive —nd f—st hy˜rid fuzzy elgorithm for
modelling is developed —nd proposed in this thesisF „he qu—dri™eps mus™les —re used
˜e™—use their dimensionD whi™h help to ™hoose the desired mus™le to ˜e stimul—tedF
„he ™hoi™e of desired mus™le to ˜e stimul—ted is not possi˜le in ™—se of m—ny sm—ll
mus™les th—t —re lo™—ted togetherF „he p—r—meters of this hy˜rid fuzzy identi(erE
model —re o˜t—ined using gener—ted pun™tion—l ile™tri™—l ƒtimul—tion @FES A impulses
—s —n input setD —nd the me—sured kneeEjoint —ngle —s —n output setF „he e0™ien™y
of this fuzzy identi(erEmodel representing nonEline—r inputEoutput dyn—mi™s depends
on the fuzzy p—rtition of its inputEsp—™e @the initi—lis—tion of premise fuzzy sets is —n
import—nt issue in fuzzy modelingAF ren™e ‚—pid €rototyping method is introdu™ed
in this proposed —lgorithm to perform this initi—lis—tion of premise fuzzy setsF sn
this proposed —lgorithm three te™hniquesX ‚—pid €rototyping —lgorithmD qr—dient
hes™ent method —nd ve—st ƒqu—res istim—tor —re ™om˜ined —s — hy˜rid —lgorithm
to —™hieve this modelling t—skF „he m—in issues of this studyD ™on™ern the kneeEjoint
dyn—mi™s identi(™—tionD —re developed for further ™ontrolE—ppli™—tion of the hum—n
kneeEjoint movements ˜y pun™tion—l ile™tri™—l ƒtimul—tion @FES AF
Table of Contents

Acknowledgements                                                                                     i

Zusammenfassung                                                                                    iii

Abstract                                                                                           vii

Table of Contents                                                                                  xi

1 Introduction                                                                                      1

2 State of the art of myoelectrical hand prostheses and exoskeleton
  devices                                                           7
  PFI   sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   F    U
  PFP   gommer™i—lly —v—il—˜le h—nd prostheses F F F F F F F F F F F       F   F   F   F   F   F    W
        PFPFI „he h—nd WIME @t—p—nA F F F F F F F F F F F F F F            F   F   F   F   F   F    W
        PFPFP „he sensorEh—nd with SUVA „e™hnologyD qerm—ny                F   F   F   F   F   F    W
        PFPFQ RSL ƒteeper €rostheses …u F F F F F F F F F F F F F          F   F   F   F   F   F   II
        PFPFR gon™lusion F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   IP
  PFQ   sntelligent h—nd prostheses in the l—˜or—tories F F F F F F F      F   F   F   F   F   F   IP
        PFQFI „he h—nd MARCUS F F F F F F F F F F F F F F F F F            F   F   F   F   F   F   IQ
        PFQFP „he h—nd of KFZD qerm—ny F F F F F F F F F F F F F           F   F   F   F   F   F   IQ
        PFQFQ RTR-2D ‚eh—˜ilit—tion „e™hnology ‚ese—r™hD st—li—n           F   F   F   F   F   F   IR
        PFQFR r—ndEprosthesis of Hokkaido university @t—p—nA F F           F   F   F   F   F   F   IS
        PFQFS hie r—nd von SouthamptonD @UK A F F F F F F F F F            F   F   F   F   F   F   IT
        PFQFT gon™lusion F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   IV
  PFR   iwq ™ontrolled r—ndEixoskeleton devi™es F F F F F F F F F          F   F   F   F   F   F   IV
        PFRFI Carnegie Mellon ixoskeleton @€itts˜urgh …ƒeA F F             F   F   F   F   F   F   IW
        PFRFP €olite™ni™o di wil—no ixoskeleton F F F F F F F F F F        F   F   F   F   F   F   IW
        PFRFQ gon™lusion F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   PH

                                           xi
        xii                                                                 gyx„ix„ƒ



  PFS   r—nd €rostheses „ypes F F F F F F F F F F F F F F F F F F F F F F F F F F            PI
        PFSFI iwq sign—ls don9t ™orrespond to movement9s mus™les F F F F F                   PI
        PFSFP iwq sign—ls ™orrespond to movement9s mus™les F F F F F F F F                   PP

3 EMG signal acquisition                                                                     23
  QFI   sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   PQ
  QFP   ƒurf—™e iwq sign—l ™h—r—™teristi™s F F F F F F F F F F F F F F F F       F   F   F   PT
  QFQ   p—™tors —'e™ting iwq sign—l me—surement F F F F F F F F F F F F          F   F   F   PU
        QFQFI ile™trodes F F F F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   PU
        QFQFP empli(er te™hnology F F F F F F F F F F F F F F F F F F F F        F   F   F   PV
        QFQFQ wovement —rtif—™ts F F F F F F F F F F F F F F F F F F F F F       F   F   F   PW
        QFQFR histur˜—n™es F F F F F F F F F F F F F F F F F F F F F F F F       F   F   F   QH
        QFQFS gross t—lk F F F F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   QI
  QFR   ixperiment—l re™ording equipment @Digitimer Neurolog System A            F   F   F   QI
  QFS   pun™tion—l —n—tomy of h—nd —nd fore—rm F F F F F F F F F F F F F         F   F   F   QR
  QFT   gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   QU

4 Signal processing and feature extraction                                                   39
  RFI   sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F         QW
  RFP   hete™tion of —™tiv—tion period F F F F F F F F F F F F F F F F F F F F F F           RH
        RFPFI gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F           RS
  RFQ   pilter design F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F        RT
        RFQFI yptimised (lter design F F F F F F F F F F F F F F F F F F F F F F             RW
        RFQFP FIR E80th —nd IIR E6th order (lter responses for di'erent window
                types F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F        SQ
        RFQFQ yrder e'e™t of IIR Eellipti™ (lter F F F F F F F F F F F F F F F F F           SR
        RFQFR i'e™t of di'erent (lter window types F F F F F F F F F F F F F F               ST
        RFQFS €—ssE˜—nd e'e™t of IIR Eellipti™ (lter F F F F F F F F F F F F F F F           SU
        RFQFT gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F           SW
  RFR   ƒign—l —n—lysis —nd fe—ture extr—™tion F F F F F F F F F F F F F F F F F F           TH
        RFRFI sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F F F F F F           TH
        RFRFP „ime dom—in fe—ture extr—™tion F F F F F F F F F F F F F F F F F               TP
        RFRFQ prequen™y dom—in fe—ture extr—™tion F F F F F F F F F F F F F F                TR
                —A prequen™y dom—in —n—lysisX F F F F F F F F F F F F F F F F F F            TR
                ˜A sinusoid—l h—rmoni™ w—ves F F F F F F F F F F F F F F F F F F             TT
                ™A prequen™y dom—in fe—ture extr—™tion F F F F F F F F F F F F F             TU
        RFRFR „imeEfrequen™y dom—in fe—ture extr—™tion F F F F F F F F F F F                 UP
                —A „imeEfrequen™y dom—in —n—lysis F F F F F F F F F F F F F F F              UP
                ˜A sinusoid—l h—rmoni™ w—ves F F F F F F F F F F F F F F F F F F             US
gyx„ix„ƒ                                                                             xiii



                ™A pe—ture extr—™tion F F F F F F F F F F F F F F F F F F F F F F F                   UT
        RFRFS   gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F                  UW

5 Feature input space reduction                                                                      81
  SFI   sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   F   F    VI
  SFP   €roje™tion method F F F F F F F F F F F F F F F F F F F F F      F   F   F   F   F   F   F    VP
  SFQ   PCA illustr—tion F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   F    VQ
        SFQFI elgorithm9s steps illustr—tion F F F F F F F F F F F       F   F   F   F   F   F   F    VR
        SFQFP qr—phi™—l determin—tion of eigenve™tors F F F F F          F   F   F   F   F   F   F    WH
  SFR   i0™ien™y of proje™tion method F F F F F F F F F F F F F F        F   F   F   F   F   F   F    WQ
        SFRFI €ro˜lem illustr—tion F F F F F F F F F F F F F F F F       F   F   F   F   F   F   F    WR
        SFRFP pe—tures ™onsidered sep—r—tely F F F F F F F F F F F       F   F   F   F   F   F   F    WS
               IA ve—rning †e™tor u—ntiz—tion ™l—ssi(er model F         F   F   F   F   F   F   F    WS
               PA wultiEv—yer €er™eptron networks F F F F F F F F        F   F   F   F   F   F   F   IHP
               QA ‚—di—l f—sis pun™tion networks F F F F F F F F F       F   F   F   F   F   F   F   IHR
               RA gomp—rison of LVQ, MLP —nd RBF methods                 F   F   F   F   F   F   F   IHS
        SFRFQ pe—tures ™onsidered together in Th input sp—™e F           F   F   F   F   F   F   F   IHT
        SFRFR pe—ture sp—™e redu™ed in Ph sp—™e F F F F F F F F          F   F   F   F   F   F   F   IHT
  SFS   ‚esults dis™ussion F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   F   F   IHU
  SFT   gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   F   F   IIH

6 Performances of proposed FTMC algorithm                                                            113
  TFI   sntrodu™tion F F F F F F F F F F F F F F F F F F F F F   F F F F F   F   F   F   F   F   F   IIQ
  TFP   xeur—l xetwork ƒystems F F F F F F F F F F F F F F       F F F F F   F   F   F   F   F   F   IIR
        TFPFI er™hite™ture F F F F F F F F F F F F F F F F F     F F F F F   F   F   F   F   F   F   IIS
        TFPFP ix—mple of illustr—tion F F F F F F F F F F F      F F F F F   F   F   F   F   F   F   IIS
               IA ve—rning pro™edure to (nd optimised w1         —nd w2      F   F   F   F   F   F   IIT
               PA heriv—tiveE˜—sed optimis—tion method F         F F F F F   F   F   F   F   F   F   IIU
        TFPFQ qr—dientE˜—sed optimis—tion methods F F F          F F F F F   F   F   F   F   F   F   IPH
               IA w—them—ti™—l des™ription F F F F F F F F       F F F F F   F   F   F   F   F   F   IPI
  TFQ   xeuroEfuzzy systems F F F F F F F F F F F F F F F F      F F F F F   F   F   F   F   F   F   IPQ
        TFQFI xeuroEfuzzy systems —r™hite™ture F F F F F         F F F F F   F   F   F   F   F   F   IPT
        TFQFP xeuroEfuzzy systems optimis—tion F F F F F         F F F F F   F   F   F   F   F   F   IPW
  TFR   xotion of interpret—˜ility F F F F F F F F F F F F F F   F F F F F   F   F   F   F   F   F   IQH
        TFRFI snput fuzzy sets initi—lis—tion F F F F F F F      F F F F F   F   F   F   F   F   F   IQI
        TFRFP w—them—ti™—l des™ription F F F F F F F F F         F F F F F   F   F   F   F   F   F   IQS
        TFRFQ €—r—meters identi(™—tion F F F F F F F F F F       F F F F F   F   F   F   F   F   F   IQU
               —A vine—r p—r—meters identi(™—tion F F F F        F F F F F   F   F   F   F   F   F   IQV
               ˜A xonline—r p—r—meters identi(™—tion F F         F F F F F   F   F   F   F   F   F   IRI
        xiv                                                                  gyx„ix„ƒ



        TFRFR gomplexity —nd interpret—˜ility ™onsider—tion in ˜oth FSC —nd
              FTMC models F F F F F F F F F F F F F F F F F F F F F F F F F F                    IRS
              —A FTMC fuzzy ™l—ssi(erEmodel F F F F F F F F F F F F F F F F F                    IRU
              ˜A puzzy su˜tr—™tive ™lustering @FSC A F F F F F F F F F F F F F                   ISP
        TFRFS gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F               ISQ
  TFS   gomp—rison ˜tween MLP, RBF, LVQ and FTMC F F F F F F F F F F F                           ISR
        TFSFI €roposed FTMC ™l—ssi(erEmodel F F F F F F F F F F F F F F F F                      ISS
              —A sniti—l fuzzy @FTMC A ™l—ssi(erEmodel F F F F F F F F F F F F                   ISS
              ˜A yptimised FTMC ™l—ssi(erEmodel F F F F F F F F F F F F F F                      ISV
        TFSFP wulti l—yer per™eptron ™l—ssi(erEmodel F F F F F F F F F F F F F                   ITH
        TFSFQ ‚—di—l f—sis xetworks ™l—ssi(erEmodel F F F F F F F F F F F F F                    ITQ
        TFSFR ve—rning †e™tor u—ntiz—tion ™l—ssi(erEmodel F F F F F F F F F                     ITS
        TFSFS gl—ssi(™—tion —™™ur—™y ™omp—rison F F F F F F F F F F F F F F F                    ITV
        TFSFT gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F               ITV

7 Inuence evaluation of important parameters                                                    171
  UFI   sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   IUI
  UFP   prequen™y f—ndp—ss e'e™t F F F F F F F F F F F F F F F F F F F       F   F   F   F   F   IUR
        UFPFI gl—ssi(™—tion perform—n™e with RBF E˜—sed —ppro—™h             F   F   F   F   F   IUS
        UFPFP gl—ssi(™—tion perform—n™e with FSC E˜—sed —ppro—™h             F   F   F   F   F   IUT
        UFPFQ gl—ssi(™—tion perform—n™e with FTMC —lgorithm F F              F   F   F   F   F   IUU
        UFPFR gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   IUV
  UFQ   „hreshold level e'e™t F F F F F F F F F F F F F F F F F F F F F F    F   F   F   F   F   IUV
        UFQFI gl—ssi(™—tion perform—n™e with RBF E˜—sed —ppro—™h             F   F   F   F   F   IUW
        UFQFP gl—ssi(™—tion perform—n™e with FSC E˜—sed —ppro—™h             F   F   F   F   F   IVH
        UFQFQ gl—ssi(™—tion perform—n™e with FTMC —lgorithm F F              F   F   F   F   F   IVI
        UFQFR gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   IVI
  UFR   foth sign—l length —nd s—mpling frequen™y e'e™ts F F F F F F         F   F   F   F   F   IVP
        UFRFI gl—ssi(™—tion perform—n™e with RBF E˜—sed —ppro—™h             F   F   F   F   F   IVQ
               —A g—se of fe—tureEgroup M0, M1 and M2 F F F F F F            F   F   F   F   F   IVQ
               ˜A g—se of Eng fe—ture F F F F F F F F F F F F F F F F F      F   F   F   F   F   IVR
        UFRFP gl—ssi(™—tion perform—n™e with FSC E˜—sed —ppro—™h             F   F   F   F   F   IVS
               —A g—se of fe—tureEgroup M0, M1 and M2 F F F F F F            F   F   F   F   F   IVS
               ˜A g—se of Eng fe—ture F F F F F F F F F F F F F F F F F      F   F   F   F   F   IVT
        UFRFQ gl—ssi(™—tion perform—n™e with FTMC —lgorithm F F              F   F   F   F   F   IVU
               —A g—se of fe—tureEgroup M0, M1 and M2 F F F F F F            F   F   F   F   F   IVU
               ˜A g—se of Eng fe—ture F F F F F F F F F F F F F F F F F      F   F   F   F   F   IVU
        UFRFR gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F     F   F   F   F   F   IVW
gyx„ix„ƒ                                                                                    xv



  UFS    gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F IWH

8 Musculoskeletal dynamics identication                                                                 191
  VFI  sntrodu™tion F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   F   F    F   F   IWI
  VFP  pound—tions —nd wethods F F F F F F F F F F F F F F F        F   F   F   F   F   F   F    F   F   IWQ
  VFQ  ixperiment—l setup —nd pro™edure F F F F F F F F F F         F   F   F   F   F   F   F    F   F   IWS
  VFR   worphologi™—l models F F F F F F F F F F F F F F F F F      F   F   F   F   F   F   F    F   F   IWW
  VFS  €roposed hy˜rid fuzzy modelling —lgorithm F F F F F F        F   F   F   F   F   F   F    F   F   PHI
  VFT  ‚ules ™onsequent p—r—meters initi—lis—tion using ‚€e         F   F   F   F   F   F   F    F   F   PHQ
  VFU  ry˜rid —lgorithm steps F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   F    F   F   PHR
  VFV  wethodology F F F F F F F F F F F F F F F F F F F F F F      F   F   F   F   F   F   F    F   F   PHS
  VFW  yptimis—tion of sele™ted model F F F F F F F F F F F F       F   F   F   F   F   F   F    F   F   PHU
  VFIH ry˜rid model v—lid—tion F F F F F F F F F F F F F F F F      F   F   F   F   F   F   F    F   F   PHV
       VFIHFI ƒign—l Test-SC1 F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   F    F   F   PHW
       VFIHFP ƒign—l Test-A F F F F F F F F F F F F F F F F F F     F   F   F   F   F   F   F    F   F   PIH
       VFIHFQ ƒign—l Test-PRBS F F F F F F F F F F F F F F F        F   F   F   F   F   F   F    F   F   PII
  VFII gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F   F   F   F   F   F   F   F    F   F   PII

9 Conclusions and future works                                                                           213
  WFI    ‚e™—pitul—tion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PIQ
  WFP    ‡h—t —re the —ppli™—tions of this „hesis F F F F F F F F F F F F F F F F PIU
  WFQ    „he go—l of this rese—r™h —nd future works F F F F F F F F F F F F F F F PIW

Bibliography                                                                                             221
Chapter 1
Introduction

„he use of neuromus™ul—r sign—ls —nd identi(ed wus™uloskelet—l systems in upper

extremity —nd lowerEextremity o'er — new gener—tion of —ssistive te™hnology for ˜oth

he—lthy —nd dis—˜led peopleF pirstD they —id dis—˜led persons in reg—ining lost fun™E

tion or improving their —™tivity of d—ily living life —nd for —ssessing reh—˜ilit—tion

progressF ƒe™ondD they ™—n ˜e introdu™ed in setting the hum—n m—™hine interf—™e

using neuromus™ul—r sign—ls —s ™omm—nd sign—ls for the exoskeleton devi™esF

sn ™h—pter P it is des™ri˜ed (rst the st—te of the —rt ™on™erning myoele™tri™ prosthesesD

whi™h —re used to restore the fun™tion—lity of —n —mput—ted h—ndF ƒe™ondD the st—te

of the —rt of myoele™tri™EexoskeletonsD whi™h —re used —s hum—nEm—™hine interf—™esF

„hese devi™es ™—n ˜e —˜le to re™ognise the desired movements of the oper—tor —nd —sE

sist ˜oth he—lthy —nd dis—˜led peopleF „hey —re ™onsidered —lso —s hum—n movement

—mpli(erF „he study of the (rst p—rt of movement re—lis—tionD using ele™tromyogr—ph

@iwqA sign—ls to re™ognise —nd ™l—ssify di'erent h—nd movementsD needs (rst to proE

™eed with sign—l —™quisitionF „his t—sk is of — gre—t import—n™eF „he study of iwq

sign—l —™quisition is des™ri˜ed in ™h—pter QF sn this ™h—pterD the fore—rm mus™les —™tivE

ity ™—n ˜e re—d —s ele™troEmyogr—phi™ @iwqA sign—ls vi— surf—™eEele™trodes —tt—™hed

                                           I
        P                                                            IFH   sntrodu™tion



to the fore—rm mus™lesX „hese iwq sign—ls ™—n ˜e then —n—lysed for further ™l—ssiE

(™—tion t—sksF heveloping ile™troEmyogr—phEh—nd prosthesis h—s — pro˜lem with the

re—lis—tion of performed gr—sping ™—p—˜ilityD whi™h is still — study su˜je™tF „his pro˜E

lem of performed gr—sping m—nipul—tion with independent (nger movements h—s ˜een

investig—ted in this (rst p—rtF „he popul—rity of designing —nd ˜uilding h—nd prostheE

sis is —™hieved ˜y — num˜er of universities —nd rese—r™h ™entres th—t h—ve prosthesis

h—nds n—med —fter themF sn the p—stD the h—ndEprostheses were limited on motion in

one degree of freedom —nd were ˜—si™—lly only motorised hooksF xow m—ny rese—r™h

l—˜or—tories try to perform volunt—ry ™losing —nd opening h—ndEprostheses ˜—sed on

iwq neuromus™ul—r sign—ls of fore—rm mus™lesF „he ™ontrol of h—ndEprostheses exist

in two ™—tegoriesD the (rst is ™onvention—l ˜odyEpowered prosthesesD whi™h —re powE

ered —nd ™ontrolled ˜y gross ˜ody movements —s me™h—ni™—l ™omm—ndsD usu—lly of the

shoulderF „he se™ondD wyoele™tri™—l prosthesesD present the ˜est ™onsidered w—y to

restore the fun™tion—lity of —n —mput—ted h—ndF „hese h—ndEprosthesesD whi™h ˜elong

to this se™ond ™—tegory —re divided into two typesF „he (rst type exploit iwq sign—ls

th—t —re not issued from mus™les responsi˜le for ™orresponding movementD ˜ut from

—ny mus™les usu—lly ˜i™epsF ƒu™h type of prosthesis use iwq sign—ls only —s swit™h

impulsesF „he se™ond type of wyoele™tri™—l h—ndEprostheses —re —˜le to re™ognise the

desired movement from iwq neuromus™ul—r sign—ls issued from group of mus™les

responsi˜le for ™orresponding movementsF „he (rst p—rt of this thesis ™onsiders this

se™ond type of myoele™tri™ h—ndEprostheses ™ontrolF sf — m—™hine ™—n underst—nd huE

m—n movementD it ™—n ˜e used in reh—˜ilit—tion —s — person—l tr—iner th—t interprets

— p—tient9s iwq sign—ls —nd help to provide — right movementF „he most e'e™tive
                                                                             Q



reh—˜ilit—tion methods employ iwqEm—™hine —ssisted exer™isesD to improve the fun™E

tion—l ™—p—™ity —nd strengthen the —'e™ted mus™lesF sn the s—me w—y it ™—n —lso ˜e

used to ™ontrol leg exoskeleton devi™esD th—t ™—n ˜e —˜le to support the leg mus™les

during ™ommon movements like getting up from — ™h—irD w—lking —nd ™lim˜ing st—irsF

st9s import—nt to mention th—t the leg9s neuromus™ul—r iwq sign—ls —re more e—sily

re™ognised th—n those of the fore—rm9s neuromus™ul—r iwq sign—lsF

ixtr—™ted fe—tures in timeED frequen™yE —nd timeEfrequen™yEdom—in will ˜e des™ri˜ed

—nd ™omp—redD see ™h—pter RD to (nd the relev—nt onesD whi™h —re —˜le to dis™rimin—te

these movement ™l—sses in ™le—r sep—r—ted ™lustersF pinding the ˜est fe—ture distriE

˜utionD whi™h h—s the ˜est dis™rimin—tion ˜etween ™l—sses is — ™ru™i—l step ˜efore

sele™ting the ™l—ssi(™—tion te™hnique for the spe™i(™ t—sk of ™ontrolF

„his study goes forw—rd —nd investig—tes the re™ognition ™—p—˜ilityD whi™h is dependE

ing on the num˜er of ™h—nnels used for ™olle™ting iwq sign—lsF „his re™ognition

™—p—˜ility in™re—ses with the num˜er of me—surement ™h—nnelsF sn this thesisD it is

shown th—t with only two ™h—nnels it is possi˜le to re™ognise —nd ™l—ssify h—nd —nd

—lso (nger )exion movementsD whi™h —re thum˜ED pointerE —nd middleE(ngerF qenE

er—llyD in other pu˜lished studiesD the num˜er of me—surement ™h—nnels —re —t le—st

four ™h—nnelsF „hereforeD it is ne™ess—ry to t—ke — p—rt of the study for the e'e™t

ev—lu—tion of the fe—ture sp—™eEdimensionF sf this fe—ture sp—™eEdimension in™re—sesD

its in)uen™e on dis™rimin—tionE—™™ur—™y will ˜e positiveD ˜ut this in™re—sing of sp—™eE

dimension h—s — dr—w˜—™k reg—rding time ™onsumingF por this question we h—ve two

solutionsX either to t—ke — l—rge fe—ture sp—™eEdimension —nd then to —pply sp—™eE

redu™tion methods like €rin™iple gomponent en—lysis @€geAD or to ™onsider — sm—ll

sp—™eEdimensionD see our pu˜li™—tion ‘UR“F „his study will ˜e det—iled in ™h—pter S to
        R                                                           IFH   sntrodu™tion



™omp—re ˜etween them —nd to give very import—nt resultsF

„he present—tion of these iwq sign—ls in di'erent dis™rimin—ted ™lusters ™orrespondE

ing to their movement ™l—sses is possi˜le with help of extr—™ted inform—tion from their

v—rious sign—l ™h—r—™teristi™sD p—rti™ul—rly in timeEfrequen™y dom—inF „his represenE

t—tion will ˜e useful to m—p out —nd ™ontrol h—nd prostheses or exoskeleton devi™esD

whi™h requires —dv—n™ed ™omput—tion—l methods for —™quisitionD —n—lysisD de™ompoE

sitionD —nd ™l—ssi(™—tionF sntelligent ™omput—tion—l —lgorithmsD des™ri˜ed —nd ™omE

p—red in ™h—pter TD —re those ˜—sed on neur—l networks like wultiEv—yer €er™eptron

@wv€AD ‚—di—l f—sis xetworks @‚fpA —nd ve—rning †e™tor u—ntiz—tion network

@v†AF „he others —re ˜—sed on puzzy logi™ like puzzy ƒu˜tr—™tive glustering @pƒgA

—nd proposed puzzy „rimmed we—n gl—ssi(™—tion @p„wgA —lgorithmD see our pu˜E

li™—tions ‘UQ“ ‘US“F „his proposed intelligent ™l—ssi(er —ppro—™hD ˜—sed on trimmed

me—n ™lustering —nd fuzzy logi™D will ˜e —lso ™omp—red with —˜ove ™ited intelligent

™omput—tion—l methods to ˜e ev—lu—tedF

sn ™h—pter U — gener—l study of some import—nt p—r—metersD whi™h h—ve — gre—t inE

)uen™e on ™l—ssi(™—tion perform—n™es is ™onsideredF „hese p—r—meters should ˜e opE

timised to perform the ™l—ssi(™—tion —™™ur—™y resultsF ƒome of these p—r—meters —reX

p—ssE˜—nd frequen™yD (lterEtypeD ˜eginning p—rt length of iwq sign—lD noise ˜—seEline

referen™eD —nd frequen™y s—mplingF „his study —llows us to get — glo˜—l view —˜out

how to ™hoose the v—lues of these p—r—meters in order to get the ˜est ™l—ssi(™—tion

—™™ur—™yF



wodels ev—lu—tion of mus™uloskelet—l stru™tures is ™onsidered in the se™ond p—rt of
                                                                             S



this thesisF „he piƒ pro™edure should stimul—te the mus™les @qu—dri™eps —s —ppliE

™—tionA —t the ™orre™t time during w—lking F „o perform this t—sk of syn™hronis—tion

—nd to —ssess the st—˜ility of w—lkingD — right mus™uloEskelet—lEmodel is needed for

r—pid —nd dyn—mi™ —djustments to ™orre™t —nd ™ontrol the motion of lim˜ segments

—nd ™onsequently the ˜odyF e proposed performed mus™uloEskelet—l identi(erEmodel

for qu—dri™ep mus™les properties ˜—sed on proposed fuzzyEmodeling elgorithm see

our pu˜li™—tions ‘UP“ —nd ‘IT“D is des™ri˜ed in ™h—pter VF „his model uses pun™E

tion—l ile™tri™—l ƒtimul—tion @piƒA —s input set —nd kneeEjoint —ngle —s output setF

„he mus™les of legs —nd —rms —re enough ˜igD whi™h —llows the use of this method

for stimul—ting ex—™tly the desired mus™leF pun™tion—l ele™tri™—l stimul—tion @piƒA

impulses h—ve ˜een used to —™tiv—te mus™les dis—˜led ˜y spin—l ™ord injuriesF ƒtimuE

l—tors worn on the legD whi™h stimul—te mus™les through ele™trodes ™—n help to restore

or perform mus™le —™tiv—tion for w—lkingF

„he l—st ™h—pterD will ™on™ern the re™—pitul—tion of —ll this thesis —nd moreover gives

the re—l —ppli™—tions of this study —nd the —ttempted future workF
T   IFH   sntrodu™tion
Chapter 2
State of the art of myoelectrical hand
prostheses and exoskeleton devices

2.1 Introduction
„he rese—r™h in 4myoEprostheses4 is p—rt of — l—rger trend in hum—nEm—™hine interE

—™tion th—t —ims to integr—te ˜odyD mus™le —nd m—™hineF pirst go—l of this rese—r™h

is fo™used on the ™l—ssi(™—tion @re™ognitionA of myoele™tri™ sign—ls for further ™ontrol

of h—ndEprosthesesF st is expe™ted to —dv—n™e in this ™h—pter the st—te of the —rt

—˜out tod—y9s most ™ommon ™ommer™i—lly —v—il—˜le myoele™tri™—lEprosthesesF ƒin™e

IWUH — ˜ig progression is done in this (eldF sn the ˜eginning they were limited on

motion in one degree of freedom —nd —re ˜—si™—lly motorized hooksF xow ˜y use of —

suit—˜le ™om˜in—tion of ele™troni™ h—rdw—re —nd softw—reD it is possi˜le to re™ognise

the myoele™tri™ fe—tures of —t le—st two di'erent grips in re—l timeD with —n —™™ur—™y

of —lmost WS per™entF purther rese—r™hes might eventu—lly in™lude ™omfort—˜le h—ndE

prostheses th—t ™ould —™tD in — ne—rly lifelike m—nner —nd in re—l time of —s m—ny —s

six di'erent gripsF yn other side „he designs of m—jority of ™ommer™i—lly —v—il—˜le

ele™tri™—l h—ndEprostheses do not provide independent ™ontrol of (ngers —nd thum˜s

                                           U
                PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
         V                                                                      devi™es


˜ut most of them —re ™—p—˜le of only simple one degree of freedom gripsF ixperts in

prostheses gener—lly —gree th—t the ele™tri™—l h—nd prostheses should respond to the

following ™riteri— whi™h —re vit—l to — person9s d—ily —™tivitiesX


   • rel—tively ™omp—r—˜le to the weight of hum—n h—nd @low weightAF


   • rel—tively ™omp—r—˜le —lso to the size of hum—n h—nd @low sizeA


   • —ppe—r—n™e s—tisf—™tion for the p—tient @™osmeti™A


   • don9t ˜e — sour™e of noisy sounds @noiselessnessA


   • h—ve su0™ient —utonomy in energy


   • h—ve — time of re—™tion —s short —s possi˜leD ide—lly re—l timeF


   • reli—˜le


„he se™ond —ppli™—tion of iwq sign—ls re™ognition is reh—˜ilit—tion issueD see se™tion

PFRF „here is — growing need for physi™—l reh—˜ilit—tion —nd —ssist—n™e to improve the

qu—lity of life for physi™—lly dis—˜led peoplesF ƒever—l exoskeleton devi™es ‘SI“ ‘TS“

‘IV“ in ro˜oti™ systems for reh—˜ilit—tion h—ve ˜een ™onstru™ted to perform reh—˜ilit—E

tion support systems —nd m—ny works in this topi™ —re done during the two l—st ye—rsF

ƒome of them ‘IV“ exploit iwq sign—ls th—t —re not issued from mus™les responsi˜le

on ™orresponding movementD ˜ut from ˜i™epsF „hese —uthors fo™used their —ttention

on — ˜—si™ pin™hing motion ˜etween the index (nger —nd the thum˜F „he —mpli(edD

(ltered —nd norm—lised iwq sign—l me—sured from ˜i™eps ™—n ˜e used to ™ontrol

the exoskeleton devi™esF yther works ‘RV“ ‘U“ ™onsider the re™ognition of desired
PFPF gommer™i—lly —v—il—˜le h—nd prostheses                               W



movement using iwq sign—ls issued from some —rmEmus™les responsi˜le on ™orreE

sponding movementsF sn these ™—ses iwq sign—lsD —re simply re™ti(ed —nd (ltered

then ™omp—red to — de(ned threshold to ™ontrol the —™tu—tors of the exoskeletonF



2.2 Commercially available hand prostheses

2.2.1 The hand WIME (Japan)
es —n —ppli™—tion for the study of —rti(™i—l h—nds —nd the study of upperElim˜ prosE

thesesY the ‡r @‡—sed— r—ndA series w—s st—rted in IWTRF „he development of the

me™h—nism of h—nds —nd their ™ontrol methods using ele™tromyogr—m w—s the m—in

pointF „heir —™hievements resulted in the WIME h—nd @‡—sed— sm—sen wyo ile™E

tri™ h—ndAD whi™h h—s ˜een ™ommer™i—lly —v—il—˜le sin™e IWUVD (gure PFIF „he WIME

rexh is — pr—™ti™—l iwqE™ontrolled fore—rm prosthesis —nd m—nuf—™tured ˜y the

Imasen ingineering gorpF ƒu0™ient (eld tests were ™—rried out during the develE

opment—l period with the ™ooper—tion of QH —mputees over — period of three ye—rsF

„he me™h—ni™—l )ipE)op —llowed gripping ˜y the (ngers —nd pin™hing ˜y three (nE

gers using only one motorD whi™h w—s volunt—rily ™ontrolled ˜y iwq sign—ls o˜t—ined

from the —rm of the —mputeeF „he pressure sensor —tt—™hed to the (ngers sensed the

re—™tion for™e of o˜je™tsD whi™h w—s then fed ˜—™k to —mputees ˜y ele™tro™ut—neous

stimul—tionF „he WIME rexh h—s ˜een ™ommer™i—lly —v—il—˜le sin™e IWUVD ‘T“



2.2.2 The sensor-hand with SUVA Technology, Germany
‰e—rs —go ‡inkler —nd fierwirth in the ƒwiss fellikon —t SUVA h—d the ide— of

feeding me—sured ”impressions of senses” ˜—™k into the h—ndEprosthesesF por the
              PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
        IH                                                                    devi™es




                      pigure PFIX essemly of the WIME rexh


(rst time this h—ndEprosthesis w—s equipped with —n —utom—ti™ grip ™ontrol systemD

(gure PFPF „he SUVA sensor is ste—dily metering the dire™tion —nd the size of the

for™eD whi™h exist ˜etween the thum˜ —nd the gripped o˜je™tF st sends no sign—l ifD in

the ™—se of sm—ll o˜je™tsD the tip of the thum˜ is not tou™hedF sn order to re™ognize

— grip nevertheless — se™ond sensorD the (nger lever sensor w—s ˜uilt into the sensor

h—ndF ‡ith this one —lso these grips —re re™ogniz—˜le —nd govern—˜leF „he me—suring

d—t— of the SUVA sensor will ˜e re—d —nd the —mount —s well the —ngle of for™e

is ™—l™ul—ted from the me—sured for™e ™omponentsF es long —s this me—sured —ngle

rem—ins under — ™riti™—l v—lue the o˜je™t does not slip from the h—ndD ‘ST“F „hese

devi™es —llow to ™—rry out two types of ™ontrolX


   • IA eutom—ti™ mode of ™ontrolX

     sn this mode the h—nd is ™losed with — m—ximum speed —nd seizes —n o˜je™t

     with the we—kest grip for™e @IH xAF sf the sensor dete™ts — ™h—nge of positionD

     it —utom—ti™—lly m—kes in™re—se the grip for™e to its m—ximum @IHH xA to —void

     the f—ll of o˜je™tsF


   • PA †—ri—˜le mode of ™ontrolX

     „he speed of opening is determined ˜y the power —nd the speed of the mus™ul—r
PFPF gommer™i—lly —v—il—˜le h—nd prostheses                                II



     sign—lF „he speed of ™losing is — fun™tion of the redu™tion of the mus™ul—r

     —™tiv—tionD ‘Q“F




                        pigure PFPX essemly of the SUVA r—nd




2.2.3    RSL    Steeper Prostheses UK
RSL ƒteeper is the prin™ip—l servi™e of reh—˜ilit—tion of the …nited uingdomF „his

™omp—ny in p—rti™ul—r designed the prostheses of IQEye—rEold eli e˜˜—sD (gure PFQD

who lost ˜oth —rms in the sr—q w—rF ho™tors pl—n to (t the teen—ger with two —rti(™i—l

—rmsD whi™h will ˜e str—pped together —nd worn somewh—t like — ru™ks—™kF yn his

rightEh—nd sideD eli will ˜e (tted with — 4myoele™tri™4 ™ontrol systemD — st—teEofEtheE

—rt te™hnology whi™h uses ele™trodes to pi™k up nerve sign—ls from existing mus™les

in the stumpF fe™—use eli9s left —rm w—s —mput—ted higher upD —t the shoulderD its

repl—™ement m—y not o'er the s—me fun™tion—lity sin™e there is less mus™le to work

withF ƒoD — tensing of the upper —rm mus™le would ™—use — motorised h—nd to gripD

while rel—xing it would rele—se the pin™er movementF „he gre—ter the tensionD the

qui™ker the motor worksF ris right h—nd ™ould ˜e wired to his ˜i™ep —nd his motorised

wrist to his tri™epsF por the el˜owD — ˜etter option might ˜e to use — simple pulley

system whi™h eli would oper—te simply ˜y shruggingF „he ele™tri™s depend on —
              PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
        IP                                                                    devi™es



lithium ion ˜—tteryD whi™h would ˜e worn in — pou™h on the upper ˜ody —nd repl—™ed

d—ilyF wr gooperD who works for the prostheti™s m—kers RSL ƒteeper s—ysX gutting

with — knife will ˜e di0™ult ˜ut he9ll ˜e —˜le to use — fork or spoon —lmost n—tur—llyD

™om˜ his h—irD type with two (ngersD ‘R“F




                       pigure PFQX RSL ƒteeper €rostheses …u




2.2.4 Conclusion
„he development —nd the improvement of three ex—mples of ™ommer™i—lly —v—il—˜le

ele™tri™—l h—nd prostheses in three di'erent ™ountriesD like qerm—nyD UK —nd Japan

—re des™ri˜edF „he study of these ™ommer™i—lly —rti(™i—l h—nds ˜eg—n with p—ssive

prosthesesD ˜ut it w—s possi˜le to develop the —™tive prostheses F „he studies h—d

—t (rst —imed only to develop m—™hines to perform motion in one degree of freedom

—nd were ˜—si™—lly motorised hooksF ‚e™ently the —im h—s ˜een to develop prostheses

th—t ™—n performD using iwq sign—lsD more ™ompli™—ted t—sksF




2.3 Intelligent hand prostheses in the laboratories
PFQF sntelligent h—nd prostheses in the l—˜or—tories                      IQ



2.3.1 The hand MARCUS
r—nd MARCUS w—s initi—lly designed like —n evolution of Otto-Bock h—ndEprothesisF

st ™onsists of three (ngersX thum˜D index —nd m—jorD (gure PFRF st h—s two degrees

of freedom —nd is driven ˜y two sep—r—ted motorsD the (rst one is responsi˜le for the

movements of the in™h —nd se™ond one —™ting in the movements of the index —nd the

m—jorD whi™h —re dependentF „he h—nd moreover is equipped with Hall-eect-sensors

to o˜t—in inform—tion on the position of the (ngers —nd — t—™tile sensor on the thum˜

giving inform—tion on the for™e of gr—spingD ‘PV“ ‘UI“ ‘RI“F




                              pigure PFRX Marcus r—nd




2.3.2 The hand of KFZ, Germany
„he h—nd of u—rlsruhe is — very light h—ndD e—™h (nger weighs only @PHgA whi™h

—pproxim—tes very well the —ptitudes of h—ndling of the hum—n h—ndD ˜y m—king it

possi˜le to move independently —ll the (ngersF st uses for th—t —n origin—l —ppro—™hY

in the pl—™e of motors with hFgF ™urrentD this h—nd h—s IV )uidi™D )exi˜le —nd mini—E

turised —™tu—tors whi™h order S (ngersF i—™h (nger ™ont—ins the —™tu—tors responsi˜le

for its in)e™tionD —nd t—™tile sensorsF „he met—™—rpus provides enough sp—™e to pl—™e

there — mi™roE™ontrollerD mi™roEv—lvesD the sour™e of energy —nd — mi™roEpumpF en
              PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
        IR                                                                    devi™es



option—l —™tu—tors —s designed to fold the wristD (gure PFSF

„he )exi˜le (ngers —re —˜le to gr—sp o˜je™ts of v—rious sizes —nd formsD ˜y distri˜utE

ing the for™e of ™ont—™t on — l—rger surf—™eF „husD th—nks to this selfE—d—pt—tionD —

l—rge v—riety of o˜je™ts ™—n ˜e seized without using sensory inform—tionF woreoverD

the surf—™e of the (ngers is soft —nd the ™oe0™ient of fri™tion is in™re—sed using —

ru˜˜ery glove whi™h ™overs the —rti(™i—l h—ndF fe™—use of )exi˜ility of the h—ndD

this one —ppe—rs more n—tur—l th—n — rigid ro˜otElike h—nd —nd the risk of the dire™t

inter—™tions with other people is minimisedD ‘SU“F




                      pigure PFSX „he h—nd of KFZD qerm—ny




2.3.3    RTR-2      , Rehabilitation Technology Research, Italian
r—nd RTR2 is ™onsisted of thum˜ —nd two identi™—l (ngersD the m—jor —nd the indexF

st h—s nine degrees of freedomD (gure PFTF ‚„‚P ™ont—ins only two motorsD for the

movements of in)e™tion —nd extension of the (ngers —nd the thum˜D —nd for the

—ddu™tion —nd the —˜du™tion of the thum˜F „he movements —re ˜—sed on — system

of tr—nsmission per tendonF „o improve the gr—sping oper—tionD the inform—tion

provided ˜y —n —rti(™i—l sensory system is ™onsideredD whi™h re—™t —utom—ti™—lly in
PFQF sntelligent h—nd prostheses in the l—˜or—tories                       IS




                               pigure PFTX RTR2 r—nd

™—se of o˜je™ts slipping from the h—nd without —ny re—™tion from the userF „he

h—nd RTR2 is equipped with position sensors —nd — tensiometer on the ™—˜le whi™h

™ontrol the pointer —nd for™e sensor on the end of the thum˜F ell sensors —nd the

two motors —re inside the stru™ture of the h—ndD ˜ut its weight rem—ins very light

sin™e it is lower th—n QPHgF prom other side the grip strength rem—ins insu0™ientX it

is of IT x where—s th—t of the ™ommer™i—l prostheses re—™hes IHH xF „he ™ontrolling

of the prosthesis t—kes pl—™e vi— — „op level gontrolling module @TCM A —nd — vow

level gontrolling module @LCM AF „he TCM uses the myoele™tri™ sign—ls @iwqA to

produ™e — ™ontrol for the LCMD whi™h regul—tes the motors —fter ™olle™tion of the

sensory sign—lsF „his h—nd is — s™heme for future wyoele™tri™ h—nd prostheti™ RTR4

—nd Cyber-hand €rotheti™D ‘IR“ ‘IP“F


2.3.4 Hand-prosthesis of Hokkaido university (Japan)
„his h—nd is developed ˜y the eutonomous ƒystems ingineering v—˜ of the Hokkaido

…niversity @t—p—nAD (gure PFUD within the fr—mework of — proje™t to design — prosthesis

of h—nd h—ving the ˜eh—vior of — n—tur—l h—nd —nd ordered ˜y iwq sign—lsF st uses —n

—djust—˜le tr—nsmission system in whi™h the ™ourse of the ™—˜le depends on the size

of the lo—dF „he (ngers move qui™kly under — light lo—d —nd slowly with — high ™ouple
              PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
        IT                                                                    devi™es



of torque under — he—vy lo—dF e method of order using tendons w—s sele™ted to lo™—te

the —™tu—tors outside the driven elementsF „he h—nd h—s U degrees of freedomD for

e—™h (nger plus the —˜du™tionG—ddu™tion of the thum˜ —nd the pron—tionGsupin—tion

of the wristF st9s ˜uilt of —luminium —nd e—™h (nger weighs PS qF ell the —™tu—tors —re

extern—l of the h—ndD the tot—l size of the h—nd is ˜igD whi™h m—kes its use impossi˜le

—s — prosthesisD ‘PP“F




pigure PFUX pi™tures of the prostheti™ h—nd developed —t the eutonomous ƒystems
ingineering v—˜ of the Hokkaido …niversityF




2.3.5 Die Hand von Southampton, (UK )
„he Southampton philosophy ™on™entr—tes on devolving the responsi˜ility of grip —dE

justment from the user to the h—nd itselfF „he intelligent h—nd uses sensorsD ele™tronE

i™s —nd mi™ropro™essor te™hnology to —llow this —d—ptive devi™e to m—int—in optimum

grip @there˜y ensuring th—t o˜je™ts do not slip from the h—ndA under the jurisdi™tion

of — st—te driven ™ontrol system @whi™h —llows e—sy ™ontrol of the prosthesisAF „he

—rti(™i—l h—nd of SouthamptonD is in development sin™e sever—l de™—desF st h—s ˜een

el—˜or—ted with the ide— to ˜e ™ontrolled in — hier—r™hi™—l w—y using iwq sign—lsF

„o gr—sp o˜je™ts with — n—tur—l h—ndD the ˜r—in must h—ve — multitude of inform—E

tion so —s to —djust the gr—sping oper—tion —nd to prevent the slipping of the o˜je™tF
PFQF sntelligent h—nd prostheses in the l—˜or—tories                         IU



roweverD with m—ny myoEele™tri™ —rti(™i—l h—ndsD to ™ontrol the for™e to ˜e exerted

˜y the h—ndD the user is —sked to use only the visu—l sign—l —s feed˜—™k sign—l while

—™ting on iwq sign—ls of fore—rmF sn order to ™ure this insu0™ien™yD the h—nd of

Southampton h—s —n intelligent devi™eX the responsi˜ility for the —djustment of the

gr—sping is ™on(ded to the h—nd itself —nd not to the userF „his devi™e uses sensorsD

ele™troni™s —nd mi™ropro™essors to m—int—in —n optim—l for™e of gr—spingD while the

user gives over—ll orders to open or ™lose using simple sign—lsF

„he h—nd of Southampton provides two types of gr—spX gr—sp with pre™ision —nd

gr—sp with for™eF „he type of gr—sping —dopted is determined ˜y the point of the (rst

™ont—™tF sf —n o˜je™t tou™hes the p—lm in (rstD the gr—sp with for™e is —ppliedY if they

—re the ends of the (ngers whi™h enter the (rst in ™ont—™tD — gr—sp with pre™ision is

usedF „he h—nd is ™losed until the o˜je™t is t—ken in the softest possi˜le w—y (gure PFV

—nd PFWF sf — slip o™™ursD it is dete™ted ˜y —™ousti™ sensors on the level of the ends of

the (ngers —nd the gr—sp is —utom—ti™—lly reinfor™edD ‘S“F




pigure PFVX pirst version of the h—nd           pigure PFWX ƒe™ond version of the h—nd
of SouthamptonF                                 of SouthamptonF
              PFH     ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
        IV                                                                      devi™es



2.3.6 Conclusion
„here —re m—ny —rti™les in the news —˜out the l—test developments in intelligent

prostheses devi™esD whi™h —re highEte™h ˜ut expensive prosthesesF „he use of — miE

™ropro™essor in the system —llows the oper—tor to supervise only the —™tions of the

h—nd while the mi™ropro™essor ™ontrols the low level re)exes of grip for™e —nd sh—peF

„he pro™essor ™—n ™ontrol more of the fun™tions of the h—nd itselfF „he oper—tor

gives simple gr—sping movement @h—nd ™losing or openingAD whi™h —re interpreted —s

™omm—nds —nd the ™ontroller ™oEordin—tes multiple degrees of freedom to sh—pe the

h—nd to m—ximise the ™ont—™t —re— ˜etween the h—nd —nd the o˜je™t —nd so minimise

™ont—™t for™esF sf the o˜je™t slips this is dete™ted —nd the ™ontroller respondsF „his

frees the user to m—ke only the str—tegi™ de™isions while the fun™tion—l r—nge is inE

™re—sedF ‡e ™—n mention here th—t these developed prostheses don9t re™ognise the

desired motion of (ngers sep—r—telyD whi™h is our (rst go—l in this rese—r™h thesisF



2.4 EMG controlled Hand-Exoskeleton devices
„he exoskeleton devi™es —re used —s —n —ssisting systems for —'e™ted people ˜y stroke

or other motor dise—ses or spin—l ™ord injureF r—ndEexoskeleton devi™es —re —n innoE

v—tive ide—s to redu™e physiother—pist intervention —nd to improve ther—py resultsF

sn this ™—se the iwq sign—ls —re used —s self ˜ody9s neur—l sign—ls to re—lise intended

h—nd movementsF ƒever—l exoskeleton devi™es in ro˜oti™ systems for reh—˜ilit—tion

h—ve ˜een ™onstru™ted to perform reh—˜ilit—tion support systemF w—ny works in this

topi™ —re done during the two l—st ye—rs —nd some of them will ˜e introdu™ed in the

following se™tionsF
PFRF iwq ™ontrolled r—ndEixoskeleton devi™es                                 IW



2.4.1    Carnegie Mellon          Exoskeleton (Pittsburgh USA)
„he me™h—ni™—l fr—mework of the exoskeleton ™onsisted of —n —luminum —n™horing

pl—te mounted to the ˜—™k of the h—nd —nd three —luminum ˜—ndsD one for e—™h of the

(nger ˜onesF „he —luminum ˜—nds —re designed to ˜e —djust—˜le for di'erent (nger

sizesF „he )exion of the €roxim—l snterph—l—nge—l @PIP A —nd hist—l snterph—l—nge—l

@DIP A joints is produ™ed ˜y steel ™—˜le running —long the front of e—™h (nger ˜—nd —nd

through to the ˜—™kside of the h—ndF „hese ™—˜les —re pulled ˜y — pneum—ti™ ™ylinder




pigure PFIHX Carnegie Mellon ixoskeletonD v—˜ of the €itts˜urgh …niversity …ƒeF


—™ting in ™ompressionF „he met—™—rpoph—l—nge—l @MCP A )exionD on the other h—ndD

is —™hieved ˜y — link—ge me™h—nismX — )o—ting link is mounted ˜etween the (nger

˜—nd ™losest to the ˜—se pl—te —nd — se™ond pneum—ti™ —™tu—torD —™ting in extension

@l—˜eled —s link—ge me™h—nismAD (gure PFIHD ‘IV“F



2.4.2 Politecnico di Milano Exoskeleton
„his exoskeletonEh—ndD (gure PFIID is ™omposed of — gloveD upon whi™h — supporting

stru™ture is ˜uiltD implemented in pl—sti™F „he pl—sti™ p—rt on the glove is used for two

re—sonsX guiding the (ngers of the p—tient in order to —™™omplish — n—tur—l movement

—nd —voiding th—t the (ngers h—d to ˜e—r —n ex™essive lo—d on their tipsF sn —ddition to
              PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
        PH                                                                    devi™es




   pigure PFIIX h—nd ixoskeletonD v—˜ of €olite™ni™o diD …niversity wil—no st—lyF

thisD two pl—sti™ ˜ended ™overs —re pl—™ed upon —nd under the fore—rm of the p—tient

—nd ˜ound together ˜y str—psF sn order to improve the system st—˜ility the upper

™over on the fore—rm is f—stened with the pl—sti™ stru™ture on the glove ˜y me—ns of

— met—lli™ ˜—rF yn the upper ™over @in the p—lm—r sideA two —™tu—tors —re f—stenedD

th—t —re Hitec servos HS-805BBF „hese ele™tri™ motors ™—n ˜e ™ontrolled in positionF

„wo wires —re joined to the (ngers tips —t one endD —nd rolled up to the pulleys of

the servos to the other endF „he wires slide through some little pl—sti™ pipes —nd

™—n tr—nsmit the m—ximum for™e produ™ed ˜y the —™tu—torsD —˜out IHH xF yne wire

is dedi™—ted to the )exion of the thum˜D while the other )exes the four (ngers —t

the s—me timeF yn the dors—l sideD two springs —re required to —llow the extension

movementsF sn this w—yD with only two —™tu—ted degrees of freedomD the devi™e is

—˜le to perform — gr—sp movementF pin—lly two potentiometers on the pulleys of the

servos —re pl—™ed in order to re™ord two position sign—ls ‘RV“F


2.4.3 Conclusion
„wo exoskeleton devi™es systems for reh—˜ilit—tion h—ve ˜een des™ri˜ed in this se™tion

to show the import—n™e of using iwq sign—ls sn order to help p—tientsD who h—d —

fun™tion dis—˜ility of their h—ndsD to get norm—l d—ily lifeF ƒu™h ixoskeleton devi™es
PFSF r—nd €rostheses „ypes                                                    PI



™ontrolled ˜y iwq sign—ls ™—n provide — selfEperforming reh—˜ilit—tion system th—t

supports the p—tients to pr—™ti™e the reh—˜ilit—tion exer™ise ˜y them selfF



2.5 Hand Prostheses Types
„he ™ontrol of h—nd prosthesis exist in two ™—tegoriesD the (rst one —re ™onvention—l

˜odyEpowered prosthesesD whi™h —re powered —nd ™ontrolled ˜y gross ˜ody moveE

mentsD usu—lly of the shoulderF „he se™ond one —re wyoele™tri™—lly ™ontrolled prosE

thesesD whi™h —re ™onsideredD —t presentD —s the ˜est w—y to restore the fun™tion—lity

of —n —mput—ted h—ndF „hese h—nd prosthesesD whi™h ˜elong to this se™ond ™—tegory

—re them self divided —lso in two typesF „he (rst type —re those exploit iwq sigE

n—ls th—t —re not issued from mus™les responsi˜le on ™orresponding movementD ˜ut

from —ny other mus™les usu—lly ˜i™epsF ƒu™h type of prostheses use iwq sign—ls only

—s swit™h impulsesF „he se™ond type of wyoele™tri™—lly h—nd prostheses —re —˜le to

re™ognise the desired movementD on the w—y —s the su˜je™t thinks —˜out moving the

prosthesisF „his ™—se is ™onsidered in this thesisF



2.5.1 EMG signals don't correspond to movement's muscles
„here is the possi˜ility to use iwq sign—ls issued from —ny p—rt of our ˜odyD for

ex—mple ˜i™epsD —s swit™h @yxEyppA sign—l to ™ontrol h—nd €rosthesesF „his type of

™ontrol is e—sierD ˜e™—use it doesn9t need —ny d—t— pro™essing ˜ut only sign—l —™quiE

sitionD re™ti(™—tion —nd then integr—tionF the re™ti(ed sign—l ™—n ˜e ™omp—red to —

threshold referen™eD if it is ˜igger then —n yx ™omm—nd is given otherwise the h—nd

prostheses is not —™tedF
              PFH   ƒt—te of the —rt of myoele™tri™—l h—nd prostheses —nd exoskeleton
         PP                                                                   devi™es



2.5.2 EMG signals correspond to movement's muscles
„he ide— in this ™—se is the use of surf—™e ele™trodes to re™ord the ele™tri™—l —™tivity

of mus™le (˜res —nd to send these sign—ls to — ™omputerD whi™h interprets them using

™onven—˜le —lgorithmsF „he —lgorithms tr—nsl—te the sign—ls into ™omm—nds th—t ™—n

™ontrol — h—nd prosthesisF „he essenti—l t—sk is ˜—sed on sign—l —™quisition —nd d—t—

pro™essingF sntended h—nd movement ™—n ˜e interpreted through the iwq sign—ls

issued from responsi˜le mus™les for su™h movementF „hese sign—ls —re dete™ted in the

region of —™tiv—ted mus™les for intended movementsF „his t—skD whi™h is ™onsidered

in this thesisD requires ˜ioEsign—l pro™essing —lgorithms for di'erent pro™essing —nd

dis™rimin—tion st—gesD whi™h ™—n ˜e resumed in the following stepsX

Steps:

   • h—t— golle™tion through sensing devi™es

   • iwq sign—l tr—nsform—tionX —n—lysis or wodeling

   • ixtr—™tion of relev—nt fe—turesD whi™h ™—n dis™rimin—te movements

   • gl—ssi(™—tionEmodels ˜uilding

   • iv—lu—tion —nd ™l—ssi(™—tion
Chapter 3
EMG signal acquisition

3.1 Introduction
„he physi™—l phenomen— o˜served gener—te often —n—logi™—l sign—lsF „he power —nd

the diversity of the re—lis—˜le tr—nsform—tions ˜y the ™omputers m—kes desir—˜le the

™onversionD (gure QFID of these —n—logi™—l sign—ls into dis™rete sign—lsD o˜t—ined ˜y

me—surements with interv—ls of regul—r timesF „his oper—tion of s—mplingD re—lised ˜y


                                     Physical
                                    phenomina
                                         x(t)
                                    Sampling
                                               x(k)
                                     Filtering
                                            y(k)

                   pigure QFIX „he (rst st—ge of sign—l —™quisition


the —n—logEtoEdigit—l ™onverters @ADC AD ™—n involve — loss of inform—tionF st is thus

—dvis—˜le to ™—rry out this oper—tion ™orre™tlyD in order not to m—ke imper™epti˜le the

                                          PQ
        PR                                                QFH   iwq sign—l —™quisition



inform—tion sought in the sign—lF „he exponenti—l in™re—se in ™omput—tion—l —˜ilities

of ™omputers —nd the —dv—n™ement of sensor te™hnology —re —ll f—™tors ™ontri˜uting

to the exp—nsion of iwq rese—r™h with (delityF iwq sign—l energy in™re—ses with

the —™tiv—tion level of — mus™leF ‡e o˜serve the v—ri—tion —lso in iwq me—surements

from experiment to experiment so the energy of —n iwq sign—l is — l—rgely qu—lit—tive

me—sureF iwq sign—ls ™—n ˜e me—sured using two ele™trode typesX

   • indwelling @(ne wire or needleA ele™trodesD whi™h —re inserted dire™tly into the

     mus™le (˜resF

   • surf—™e ele™trodesD whi™h —re pl—™ed on the skin overlying the mus™leF

„he surf—™e ele™trodes tr—nsdu™e the motor —™tion potenti—l we€D ™onverting ioni™

™urrents into ele™tri™—l ™urrentsD —nd the result—nt iwq sign—l ™—n ˜e re™orded folE

lowing —ppropri—te —mpli(™—tion —nd (lteringF rowever some distur˜—n™es m—y ˜e

introdu™ed in me—sured iwq sign—l through m—ny w—ysF pirst the hum—n ˜ody

himself is — good —ntenn—D whi™h pi™ks up ele™tri™—l sign—l emissionsD issued from

ele™tri™—l equipments in the l—˜or—toryF ƒe™ond the ™—˜les of me—surements —re good

™ondu™tors for power line noiseD SHETH rz sign—lsF eddition—lly it9s not possi˜le to

ignore the e'e™t of —rtif—™tsD whi™h —re results of ™—˜le —nd ele™trode movementsF

„he use of —v—il—˜le highly sophisti™—ted devi™es with help of the —dv—n™es m—de

in ele™troni™s te™hnology h—d m—de the —™quisition of iwq sign—l possi˜le with high

(delity —nd more e0™ien™yF qener—lly sign—ls —re the me—ns @w—ysA ˜y whi™h inform—E

tion is tr—nsmittedD whether we use the vi˜r—tions of —™™elerometersD the ele™tri™ity of

™ir™uitry or ele™tromyogr—ph @iwqA sign—ls of ele™trodsF „here —re ™ert—in fund—menE

t—l ™ommon —spe™ts of sign—ls th—t —re univers—lF ƒign—l —™quisition —nd pro™essing

—llow us to underst—nd the systemsD whi™h produ™e these sign—lsF „hereforeD the
QFIF sntrodu™tion                                                             PS



prin™iples of this oper—tion —re extremely import—nt for m—ny —spe™ts of ele™tri™—l

engineeringD —nd ™—n e—sily ˜e extended to —ny other study dom—inF

„he size of the ile™tromyogr—ph @iwqA sign—l depends onX IA the thi™kness of the

™onne™tive mus™le tissueD PA the qu—lity of the ™ont—™t ˜etween the ele™trode —nd the

skinD QA the size of the ele™trodes —nd RA the individu—l motor unit —™tion potenti—lsF

efter sign—l —™quisition —nd pro™essingD it9s possi˜le to identify —nd ™ontrol the sysE

temD whi™h is sour™e of this sign—lF fut the import—nt question explored in digit—l

—™quisition is how to s—mple —n —n—log sign—l while preserving its full inform—tionF

„he s—mpling r—te for the —n—log to digit—l ™onversion @A/D A must ˜e —t le—st twi™e

—s high —s the highest frequen™y or ˜—ndwidth of the sign—l ˜eing s—mpledD —™™ording

to Nyquist-Shannon s—mpling theoremD ‘SR“F „he knowledge of frequen™y ˜—ndwidthD

whi™h envelope the most power of iwq sign—l is ne™ess—ry to ™hoose the —ppropri—te

s—mpling frequen™yF ‡ith low s—mpling frequen™y it9s not possi˜le to tr—™k with (E

delity most r—pid ™h—nges in the sign—lD however the high s—mpling frequen™y in™re—ses

the num˜er of s—mplesD whi™h le—ds to — time ™onsumingF sn ™—se of onEline prostheses

™ontrolD the pro™edure of sign—l —™quisitionD pro™essing till de™ision ™ontrol should ˜e

short in timeF v—w s—mpling r—te me—ns time ™omput—tion ™onsumingD for whi™h the

timeEdel—yEph—se ˜etween hum—n intention of —™ting —nd prosthesis response is not

—™™ept—˜leF ƒo it should ˜e found — ™ompromise ˜etween themF „o —void —nother

undesir—˜le e'e™t of s—mplingD it9s well to employ —n —ntiE—li—sing (lter ˜efore the

sign—l is s—mpledD whi™h requires —lso — knowledge of sign—l frequen™y ˜—ndwidth of

interest in order to perform this t—skF fy de(nitionD the —ntiE—li—sing (lter ‘SR“ is used

to prevent the s—mpling of frequen™iesD in the sign—lD th—t —re higher th—n the h—lf of

s—mpling frequen™yF „hese frequen™ies will ˜e misrepresented if they —re s—mpledF por
        PT                                                 QFH   iwq sign—l —™quisition



ex—mpleD — I kHZ s—mpling frequen™y needs —n —ntiE—li—sing (lter with — ˜—ndwidth

of 500Hz @ 1 F sAD the e'e™t of this (lter is to —void the —li—sing to — lower frequen™y
           2

for the sign—ls —˜ove 500Hz due to underEs—mpling of these sign—lsF es ™onsequen™e

to this phenomenon there is the produ™tion of — new —li—sed frequen™y F aD whi™h is

— mirror of the origin—l sign—l frequen™y F —˜out 2 F sF
                                                  1




3.2 Surface EMG signal characteristics
„he me—surements of iwq sign—ls issued from mus™le ™ontr—™tions —re re—lis—tions

of — ™omplex timeEv—ri—nt pro™ess th—t ™ontrol ele™tri™—l —™tiv—tion of mus™leF „hey

provide —n —™™ess to physiologi™—l pro™esses th—t ™—use mus™les to gener—te for™esD

produ™e movementsD —nd —™™omplish fun™tions whi™h —llow us to inter—™t with the

world —round usF st9s di0™ult to dis™ern —ny distinguishing ™h—r—™teristi™s of these

sign—ls —nd it9s not —pp—rent how to qu—ntify themF ‡ith help of two nonEinv—sive

iwq surf—™e ele™trodes pl—™ed on fore—rm mus™les it9s possi˜le to dete™t iwq sign—lsD

whi™h will ˜e su˜tr—™ted ˜efore —mpli(™—tionF sn this di'erenti—l ™on(gur—tionD the

sh—pe —nd —re— of surf—™e ele™trodes —nd the dist—n™e ˜etween them —re import—nt

f—™torsD whi™h —'e™t the ™h—r—™teristi™s of this me—sured iwq sign—lF „his sign—lD

issue from — timeEv—ri—nt ™omplex dyn—mi™—l system (gure QFPD h—s —n —mplitude

in the r—nge of µVs or mVs D it depends on type —ndGor size of the mus™le —nd its

st—te @level of —™tiv—tionAF „he us—˜le spe™tre of this sto™h—sti™ @r—ndomA sign—l

™—n ˜e limited in the —re— of 20 to 500Hz D see for deep study —˜out this f—™tor the

se™tions RFQFI —nd UFPF
QFQF p—™tors —'e™ting iwq sign—l me—surement                              PU




pigure QFPX „wo ™h—nnels me—sure of r—w iwq sign—l ™orresponding to thum˜ED
pointerE —nd middleE(nger )exion movementF ƒ—mpling frequen™y equ—l to 4KHz

3.3 Factors aecting EMG signal measurement

3.3.1 Electrodes
„he form —nd the size of the surf—™e ele™trodes h—ve —n in)uen™e on me—sured iwq

sign—lF por — performed extr—™tion of qu—ntit—tive inform—tion from the iwq sign—l

it is required gre—ter fo™us on the ™on(gur—tion of the ele™trodesF „he m—jor points

to ™onsider —reX

   • ile™trodes m—teri—lX

     „wo types of surf—™e ele™trodes —re knownD IA dry ele™trodes in dire™t ™ont—™t

     with the skin —nd PA gelled ele™trodesD whi™h ™ont—in —n ele™trolyti™ gel ˜etween

     the skin —nd the met—lli™ p—rt of the ele™trodeF
        PV                                                QFH   iwq sign—l —™quisition



   • ile™trodes te™hnologyX

     st9s re™ommended th—t the ele™trodes m—ke very good ele™tri™—l ™ont—™t with the

     skin through ele™tri™—lly ™ondu™tive gelsF „hereforD the ele™trode gels m—teri—l

     should ˜e highly ™ondu™tive —nd the ele™trodes —dhesive m—teri—l should h—ve

     strong —dhesive properties to the skin for ™onsider—˜le me™h—ni™—l st—˜ility to

     —void movement —rtif—™tsF


   • ile™trodes positionX

     „he pl—™ement of ele™trode should ˜e —long the longitudin—l midline of the

     mus™leF „he longitudin—l —xis should ˜e —ligned p—r—llel to the length of the

     mus™le (˜ersF


   • ‚eferen™e ele™trode pl—™ementX

     it9s — ™ommon referen™e ele™trode to the di'erenti—l —mpli(er inputF „he pl—™eE

     ment of this ele™trode should ˜e on ele™tri™—lly neutr—l tissue @the ˜oneAF




3.3.2 Amplier technology
sn —mpli(™—tion pro™ess of sm—ll ˜ioele™tri™ sign—ls gener—ted ˜y the mus™lesD whi™h

—re typi™—lly in uV D it9s ne™ess—ry to redu™e —s possi˜le the e'e™t of noisy ele™tri™—l

sign—lsF „his t—sk is —™™omplished through the use of — di'erenti—l —mpli(erD (gure QFQD

whi™h e'e™tively ™—n™els the —m˜ient ele™tri™—l noises ™olle™ted ˜y hum—n ˜odyF „hese

—m˜ient ele™tri™—l noises ™olle™ted ˜y hum—n ˜ody ™—n re—™h the order of voltsF „his

su˜tr—™tion oper—tion of di'erenti—l —mpli(er elimin—tes these noises —nd —mplify the

sm—ll physiologi™—l sign—lsF „here —re sever—l import—nt properties to ™onsider in this

di'erenti—l —mpli(erX
QFQF p—™tors —'e™ting iwq sign—l me—surement                               PW



   • righ ™ommon mode reje™tion r—tio @CMRR A


   • †ery high input imped—n™eX —mpli(er9s input imped—n™e must ˜e higher th—n

      the imped—n™e of the ele™trodeEmus™le —re—F


   • …sing short ™onne™ting ™—˜les ˜etween sign—l sour™e @ele™trodesA —nd empli(erD

      otherwise they will ™olle™t —m˜ient noisesF


   • hg sign—lX they —re gener—ted ˜y ™hemi™—l re—™tion ˜etween skin —nd ele™trodeF


                       Muscle

                             Channel 1
                                                     ADC
                             Channel 2
                                                     ADC
                             Patient
                             Ground


                          pigure QFQX hi'erenti—l empli(er




3.3.3 Movement artifacts
„he motion of the ele™trode rel—tive to the skin produ™es motion —rtif—™tD whi™h o™™urs

in the r—nge of 0 to 15HzF por these re—sonsD the surf—™e iwq is typi™—lly (ltered

under the r—nge of PH rz to elimin—te low frequen™y noise —nd in™re—se the sign—l to

noise r—tio
        QH                                               QFH   iwq sign—l —™quisition



3.3.4 Disturbances
„he —™quisition of —n —™™ur—te iwq sign—l is very dependent on the noisy ele™tri™—l

environment —nd the perform—n™e of —™quisition instrumentsD ‘PH“ ‘SV“ ‘RS“F xoises

™—n ˜e des™ri˜ed —s —ny —spe™t of the output sign—l whi™h is undesir—˜leF ilimin—tion

of in)uen™es of these noises is not possi˜leD ˜ut it9s possi˜le to redu™e them with

ex—min—tion of ™ir™umst—n™e9s e'e™tsF „hey —re two typi™—l types of distur˜—n™esF

pirst —re ™ondu™ted distur˜—n™esD whi™h ™—n ˜e ™—used ˜y ele™tri™—l distur˜—n™es

intrinsi™ to the re™ording environment —nd it ™—n ˜e ™—used —lso ˜y the n—ture of the

re™ording devi™es themselvesF ƒe™ond —re r—di—ted distur˜—n™esD whi™h ™—n ˜e ™—used

˜y ele™trom—gneti™ emissions of environmentF

   • IA gondu™ted histur˜—n™esX

     E„r—nsdu™er noises @through the ™—˜lesA

     Eeltern—tive ™urrentD gener—ted ˜y )u™tu—tions in imped—n™e ˜etween the ™onE

     du™tive tr—nsdu™er —nd the skin @Duchene —nd GoubelD IWWQAF

     Ehire™t ™urrentD ™—used ˜y di'eren™es in the imped—n™e ˜etween the skin —nd

     the ele™trode sensorD —nd from oxid—tive —nd redu™tive ™hemi™—l re—™tions t—kE

     ing pl—™e in the ™ont—™t region ˜etween the ele™trode —nd the ™ondu™tive gel

     @Gerdle et al., 1999 AF



   • PA em˜ient histur˜—n™esX

     histur˜—n™es from the environment @ele™trom—gneti™ w—vesAD —re noises origE

     in—te from sour™es of ele™trom—gneti™ r—di—tionD su™h —s r—dio —nd television

     tr—nsmissionD ele™tri™—lEpower wiresD light ˜ul˜sD )uores™ent l—mpsD ... ‘RS“F
QFRF ixperiment—l re™ording equipment @Digitimer Neurolog System A            QI



3.3.5 Cross talk
‚e™orded iwq sign—ls —re domin—ted ˜y mus™les —™tivities sign—lsD whi™h —re ™lose

to the ele™trodeF „his re™orded iwq sign—l from desired mus™le ™ould ˜e mixed

4crosstalk 4 with other iwq —™tivities issued from one or more neigh˜oring mus™lesF

yther e'e™t of mus™les on re™orded iwq sign—ls is the dist—n™e @widthA ˜etween

the mus™le (˜res —nd ele™trodesD whi™h in™re—ses the sp—ti—l low (ltering e'e™tF „his

phenomenon is due to the f—™t th—t mus™le (˜res —™t —s low sp—ti—l (lter ‘RQ“F

„he —˜ove f—™tors illustr—te ™le—rly th—t it is not e—sy to me—sure —n ele™troEphysiologi™—l

sign—ls without distur˜—n™esF „herefor it is very import—nt to sele™t the right me—E

surement system —nd the right sensors to m—int—in optim—l ele™troEphysiologi™—l d—t—F




3.4 Experimental recording equipment (Digitimer
    Neurolog System )


iwq sign—ls —re low in —mplitude with respe™t to other —m˜ient sign—ls on the ˜ody

surf—™eD hen™e it is ne™ess—ry to dete™t the sign—l in — di'erenti—l —mpli(er ™on(gur—E

tion in order to redu™e noisesF „he ˜ipol—r re™ording te™hnique is ˜—sed on ˜ipol—r

ele™trode —rr—ngements with — di'erenti—l —mpli(erD (gure QFQD whi™h suppresses sigE

n—ls th—t —re ™ommon to ˜oth ele™trodesF gorrel—ted sign—ls ™ommon to ˜oth sitesD

power sour™es —nd ele™trom—gneti™ devi™esD —re suppressedF „he pl—™ement of ele™E

trodes is required to ˜e on the l—rge f—™e of mus™leF „he —mpli(™—tion of the two

di'erenti—l inputs should not devi—te from e—™h other more th—n 1/100000D whi™h

requires highest ™ommon mode reje™tion @CMR A possi˜leF gommon mode reje™tion

˜y —round 100dB is gener—lly su0™ient to elimin—te su™h ™ommon mode distur˜—n™esF
        QP                                                QFH   iwq sign—l —™quisition



„he CMR is expressed in log—rithmi™ form in equ—tion QFRFIF

                                                     A0
                               CM R(dB) = 20 log                                 @QFRFIA
                                                     A1

„he ˜—l—n™e in the input imped—n™e ˜etween ele™trodes m—y ˜e —n —ddition sour™e

of — su˜st—nti—l e'e™t on gener—tion of noiseF su™h pro˜lems ™—n ˜e —voided if short

™onne™tion ™—˜les ˜etween ele™trodes —nd —mpli(er —re usedF „he ˜est solution for

this pro˜lem is to use the new developed ele™trodes with in™orpor—ted —mpli(ersF



   OverviewX
sn this study the equipment of me—surement used is Digitimer NeuroLog SystemD

(gure QFRD (gure QFS —nd (gure QFT



   Modules of this equipement:

   • it h—s four ™h—nnelsF

   • —mpli(™—tion9s r—ngeX ×10 bis ×10000F

   • low ˜—nd (lter @3, 10 and 30Hz AF

   • push ˜utton for movement —rtif—™t elimin—tion for @NL824 A moduleF

   • possi˜ility of sign—l —mpli(™—tion through one or m—ny ™h—nnelsF @R ™h—nnel

     (ltersAF

   Notch Filter: this (lter is used to remove — p—rti™ul—r frequen™y from — sign—l
—nd h—s — frequen™y response th—t f—lls to zero over — n—rrow r—nge of frequen™ies @iFeF

— 50Hz not™h m—y ˜lo™k sign—ls from 49.5 to 50.5Hz AF xot™h (lter is —lso —v—il—˜le
QFRF ixperiment—l re™ording equipment @Digitimer Neurolog System A        QQ




  pigure QFRX Digitimer Neurolog SystemF iwqEwe—sureEsystem @flo™ di—gr—mmA




pigure QFSX pourEgh—nnel ssol—ted empli(er ƒystem with piltering —nd ƒign—l gonE
ditioning


in this instrumentF    „he NeuroLog ƒystem is — )exi˜le —nd upgr—de—˜le multiE

™h—nnel re™ording devi™e for rese—r™h —ppli™—tions su™h —s ele™tromyogr—phy @iwqAF

„he NL820 is the module —t the he—rt of the isol—ted —mpli(er r—nge of ™omponentsF

st is ide—l for eg ™oupled re™ording —ppli™—tions in the rese—r™h environmentF st h—s

four ™h—nnel units with independent g—in —nd (ltering ™ontrol of e—™h ™h—nnel —s well

—s — mute f—™ilityF „he NL135 psv„i‚ is — 4 channelsD se™ond order lowEp—ssD with

xot™h reje™t (lter moduleF „he (lter settings ™—n ˜e sele™tedF „herefor — rot—ry

swit™h sele™ts the IR frequen™y settings giving repe—t—˜ility over — wide r—nge with

40dB/decade —ttenu—tion —˜ove the sele™ted frequen™y v—lueF „he —™tive xot™h (lter
        QR                                              QFH   iwq sign—l —™quisition




pigure QFTX we—surements system in w—x €l—nk institute l—˜or—toryD w—gde˜urgD
qerm—ny

provides reje™tion of line frequen™y 50Hz interferen™e when swit™hed onF „he NL144

is — 4 channelsD se™ond order high p—ss (lter whi™h ™omplements the NL135 when

used with the NL820 isol—torD this module provides — ™omp—™t solution to R ™h—nnel

high —nd low p—ss (lteringF „his module designed to give g—in —nd o'set setEup

™ontrols when interf—™ing sign—ls to the —n—logEtoEdigit—l ™onverters @ADCs A of PCsF

st ™ont—ins four ™h—nnels e—™h with independently —djust—˜le (lter settings —nd front

p—nel g—in —nd o'set presetsF „here is —lso — m—ster ADC o'set ™ontrol to —llow

unipol—r ADCs to ˜e used with ˜ipol—r sign—lsF



3.5 Functional anatomy of hand and forearm
„he ingineers entrusted with the m—n—gement of the h—ndEprostheses —nd h—ndE

exoskeleton must possess — ™ompetent knowledge of the fun™tion—l —n—tomy —nd physE

iology of the h—nd —nd fore—rmD whi™h is — ™omplex ˜iologi™—l stru™tureF xe™ess—ry

—lso is the —˜ility to ™orrel—te the surf—™e topogr—phy of mus™lesD underlying mus™leE

tendon unitsD skeletonD jointsD —nd nervesF ƒo here —re some inform—tion to help to

underst—nd the me™h—ni™—l —nd —n—tomi™—l properties of the h—nd —nd fore—rm musE

™lesF „he fones of the pore—rm —nd r—nd ‘I“ —re presented in (gure QFUF „he fore—rm
QFSF pun™tion—l —n—tomy of h—nd —nd fore—rm                                QS



™ont—ins m—ny mus™les ‘QS“D — )exor of the el˜ow @brachioradialis AD —nd pronators —nd

supinators th—t turn the h—nd to f—™e upw—rds or downF sn ™rossEse™tion the fore—rm

™—n ˜e divided into two f—s™i—l ™omp—rtmentsF „he posterior ™omp—rtment ™ont—ins

the extensors of the h—ndD whi™h —re supplied ˜y the r—di—l nerveF „he —nterior

™omp—rtment ™ont—ins the )exorsD —nd is m—inly supplied ˜y the medi—n nerveF

  IF enterior gomp—rtment

        • ƒuper(™i—l qroup

             plexors of the h—nd —nd wrist
                ∗ plexor g—rpi ‚—di—lis

                ∗ €—lm—ris vongus

                ∗ plexor g—rpi …ln—ris

                ∗ plexor digitorum super(™i—lis @sublimis A

  PF €osterior gomp—rtment

        • ixtensors of the h—nd —nd wrist

             ixtensor g—rpi ‚—di—lis vongus
             ixtensor g—rpi ‚—di—lis frevis
             ixtensor higitorum @Communis A
             ixtensor higiti winimi @Proprius A
             ixtensor g—rpi …ln—ris
             e˜du™tor €olli™is vongus
             ixtensor €olli™is frevis
             ixtensor €olli™is vongus
         QT                                              QFH   iwq sign—l —™quisition



               ixtensor sndi™is @Proprius A

        • sntrinsi™ fore—rm mus™les

               fr—™hior—di—lis @te™hni™—lly — )exor of the fore—rmA

               ƒupin—tor

               en™oneus




                   pigure QFUX „he fones of the pore—rm —nd r—nd


sn ‘QS“ the glo˜—lly ™orresponding mus™les p—rti™ip—ting in (nger —nd h—nd moveE

ments —re des™ri˜edF „he following mus™lesD Flexor-digitorum-profundusD Flexor-

digitorum-supercialis —nd Flexor-polcis Elongus p—rti™ip—te in (ngers )exionF pinE

gers extension need glo˜—lly the —™tiv—tion of Extensor-digitorumD Extensor-indicis

—nd Extensor-digiti-minimiD —nd thum˜ extension needs Extensor-pollicis-longus —nd

Extensor-pollicis-brevisF

ƒurf—™e ele™trodes —re pl—™ed in the m—nner to ™over the l—rge skin surf—™e of these

mus™lesF „he lo™—tions of ele™trodes on the su˜je™t9s —rm do not isol—te — spe™iE

(ed single mus™le ˜ut ™olle™t the iwq —™tiv—tion from —ll mus™les —roundD even the
QFTF gon™lusion                                                            QU



mus™les of the deep l—yerD whi™h ™ontri˜ute to this —™tiv—tion sign—lD —lthough they

undergo — sp—™e (lteringF ƒome of these import—nt mus™lesD whi™h ™ontri˜ute in h—nd

—nd (nger motions —re presented in (gure QFV —nd (gure QFWF




            pigure QFVX ƒome pore—rm mus™les for extension movements




             pigure QFWX ƒome pore—rm mus™les for )exion movements




3.6 Conclusion
ƒurf—™e ele™trodes pl—™ed over the mus™le ™—n sense ele™tri™—l potenti—ls produ™ed

when — mus™le is ™ontr—™tedF „his sign—l dete™ted ˜y the ele™trodes is ™—lled ile™troE

wyoEqr—phi™ sign—l @iwqAF „his sign—l is re™orded —nd —mpli(ed using ™onven—˜le
           QV                                            QFH   iwq sign—l —™quisition



instrument—tionsF st should ˜e re™orded with — ™ert—in (delity to —ssure the tr—nsE

mission of its inside inform—tion @without loss of inform—tionAF „his re™ording (delity

require some fund—ment—l ™on™epts in iwq sign—l —™quisitionF woreover ™ompetent

knowledge —˜out the fun™tion—l —n—tomy of h—nd —nd fore—rm —ids to get (del iwq

sign—lsF
Chapter 4
Signal processing and feature
extraction

4.1 Introduction
„he ™hoi™e of ™l—ssi(™—tion elgorithms ˜egin with (nding the fe—tures d—t—D whi™h

™—n ˜e —v—il—˜le in sever—l formsF „hese fe—tures d—t— must ˜e ™olle™ted —nd the

question is whi™h fe—tures d—t— —re needed —nd ™—n ˜e extr—™ted —™™ording to systems

—nd ™l—ssi(™—tion pro˜lemsF wost ™l—ssi(™—tion —lgorithms —re highly sensitive to the

qu—lity of the d—t— represent—tionF sn this ™h—pter we will dis™uss iwq sign—l —n—lysis

methodsD whi™h give relev—nt fe—turesF „hese fe—tures —re used —s ™lusters for ™l—sses

re™ognitionF

„here —re m—ny sour™es of highE —nd lowEfrequen™y ™ont—min—tion on iwq sign—lsF

por ex—mple ™omputers introdu™e highEfrequen™y noises into —™quired sign—lsD espeE

™i—lly when the —™quisition ™—rd is lo™—ted within the ™omputer ™h—ssisF woreover moE

tion —rtif—™ts introdu™e —lso lowEfrequen™y noisesF qener—lly — IH till IS rz highEp—ss

(lter is used to elimin—te the movement —rtif—™ts —nd QHH till SHH rz lowEp—ss (lter is

used to elimin—te the high frequen™iesF „here —re re™ommend—tions to ™ut frequen™ies

˜elow SH rz for l—rge mus™les like for the legF rowever there —re —nother mus™les

                                          QW
        RH                             RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



in whi™h low frequen™ies ™—n h—ve relev—nt —nd useful inform—tion —˜out ™orresponE

dent movement typeF „hus the intended use of the iwq sign—ls must ˜e ™onsideredF

wore deep study —˜out (ltering e'e™t will ˜e given in this ™h—pterD se™tion RFQFP —nd

in ™h—pter U se™tion UFPF




4.2 Detection of activation period
„hreshold method whi™h ™omp—res the level of iwq sign—l with — given levelD is the

most intuitive —nd ™ommon ™omputerE˜—sed method to dete™t yxEypp timing of the

mus™le —™tiv—tion ‘RU“F „he iwq sign—l is pro™essed in the timeEdom—inF „wo (rst

tr—nsform—tions —re ™ommonly used —s prim—ry tools to —n—lyse the —™quired iwq

sign—lD whi™h —re the re™ti(™—tion —nd wEpoint moving —ver—ge pilteringD (gure RFIF

„hese prim—ry tools —re —ppropri—te —nd provide useful me—surements of the sign—l

—mplitude to dete™t the mus™les —™tiv—tion timesD whi™h —re st—rt —nd stop ph—sesF

„he moving —ver—ge (lter is the most ™ommon (lter for timeEdom—in pro™essing sign—lD




pigure RFIX pull w—ve re™ti(ed —nd (ltering of r—w iwq sign—l @r—nd ™losingA using
moving —ver—ge (lter @window a SHmsA
RFPF hete™tion of —™tiv—tion period                                       RI



(gure RFPF st oper—tes ˜y —ver—ging — num˜er of points from the input sign—l to one

point in the output sign—lD de(ned ˜y the equ—tion RFPFIF
                                              M −1
                                          1
                                   y(t) =            x(t − k)                  @RFPFIA
                                          M   k=0

where

xX is the input sign—lD

yX is the output (ltered sign—lD

wX the num˜er of points in the —ver—geD p™ @™ut o' frequen™yA a ps G wY

ps @s—mpling frequen™yA a R krzY

w @length of ‡indow A a PHH s—mples @SHmsAF

p™ a PH rzF

 sn — ™omp—rison formD (gure RFQ shows from top to ˜ottomX r—w iwq sign—lD re™ti(ed




pigure RFPX frequen™y response of the moving —ver—ge (lter with window of PHH s—mE
plesF


iwq sign—l —nd then (ltered sign—lF „he sign—l in ˜lod line in ˜ottom represents

ever—ge woving pilter response using PHH —ver—ged s—mples or — window of SHms

@s—mpling frequen™y a 4 kHz AF
        RP                             RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




pigure RFQX prom top to ˜ottomX‚—w iwq sign—lD full re™ti(™—tion iwq sign—l —nd
iwq sign—l —fter moving —ver—ge (lter —ppli™—tionF

st is possi˜le to dete™t the ˜eginning of iwq —™tiv—tion —fter the estim—tion of the

noise —mplitude th—t will ˜e ™onsidered —s threshold ˜etween —™tiv—tionEph—se —nd

noise of the sign—l iwqF ren™e ƒome knowledge —˜out the noise sign—l is required

˜efore the estim—tion of its levelF „his threshold level ™—n ˜e de(ned —s — ™ert—in

—mplitude —˜ove noise me—n v—lueD (gure RFRF „he threshold level v—lue ™—n ˜e




                    pigure RFRX xoise threshold v—lue estim—tionF


™onsidered —s — f—™tor of st—nd—rd devi—tion v—lueD @dispersionAF st is ne™ess—ry (rst
RFPF hete™tion of —™tiv—tion period                                        RQ



to re™ord — ™ert—in period of noise sign—l ˜efore iwq sign—l —™tiv—tionF „here —re

four steps for —™™omplishing this t—sk in the following w—yX

   • gentering the sign—l @me—n v—lue equ—l zeroAF

   • ‚e™tifying the sign—l @—˜solute v—lueAF

   • g—l™ul—tion of me—n v—lueF

   • g—l™ul—tion of ƒt—nd—rd devi—tionF

„he determin—tion of the yxEypp timing of the mus™le9s —™tiv—tion m—y ˜e found —s

the interse™tion ˜etweenX IA woving ever—ge †—lue @MAV A of iwq sign—l —nd PA noise

threshold levelF „hese ™urvesD (gure RFSD —re me—surements of thum˜ (nger )exion

—™tiv—tionF „his estim—tion of noise threshold v—lue is ™—l™ul—ted using noise sign—l




pigure RFSX e™tiv—tion periods determin—tion ˜—sed on estim—ted noise threshold levelF


@no mus™le —™tiv—tionA during — period of PHHH s—mples @500ms AF pigure RFS presents

from the top to ˜ottomX IA the me—sured r—w iwq sign—l of thum˜ (nger )exionD PA
        RR                              RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



(ltered iwq sign—l —nd noise threshold level in d—shed lineD QA the yxEypp timing

—™tiv—tionsF „his noise threshold level represents the ˜order ˜etween noise sign—l

—nd —™tiv—tion sign—lF „he noise referen™e level estim—tionD —nd ™onsequently initi—l

timeE—™tiv—tion of iwq sign—l is depending on —v—il—˜ility of — priori knowledge of

the sto™h—sti™ properties of noise9s —mplitudeF

gon™retely this method is not —ppli™—˜le e0™iently —lone in this w—yD ˜e™—use there

—re ™—ses in whi™h the ˜eginning of —™tiv—tion iwq sign—l presents some os™ill—tions

—˜ove —nd under the noise threshold level like in (gure RFTF „his phenomenon gives




pigure RFTX ƒome re—l os™ill—tions —˜ove —nd under the noise threshold level in the
˜eginning of yxEtiming —™tiv—tionF


—s ™onsequen™e m—ny os™ill—tions of yxEypp timing —™tiv—tionsF „hese os™ill—tions

present — ˜ig pro˜lem for the ™hoi™e of the right —™tiv—tion ˜eginning @onEtimeAF „o

resolve su™h pro˜lem it is ne™ess—ry to develop —n —lgorithm to test the dur—tion of

the —™tiv—tion period whi™h is estim—tedD in our ™—seD to ˜e 320msF „he period of

—™tiv—tion is equ—l to 320ms @IPVH s—mplesAF sf the dur—tion of yxEtimingD during
RFPF hete™tion of —™tiv—tion period                                        RS



the (rst IPV ms of QPHms f—lls down to yppEtiming then this yxEtiming —™tiv—tion

is ignoredD otherwise it will ˜e ™onsidered —s the right inst—n™eEtime of the ˜eginning

of mus™le9s —™tiv—tionF „his method gives the following positive results shown in

(gure RFUF




pigure RFUX „op (gX iwq sign—l of middle (nger )exionF widdle (gX moving —ver—ge
(ltering of this sign—lF fottom (gX ilimin—tion of os™ill—tions —˜ove —nd under the
noise threshold level in the ˜eginning of yxEtiming —™tiv—tion —nd determin—tion of
desired —™tiv—tion sign—l periodF




4.2.1 Conclusion
sn ™ontr—st to ™ommonly used thresholdE˜—sed estim—tion methods for dete™tion of

—™tiv—tion period yxEypp timingD the proposed —lgorithm proves to ˜e re—son—˜ly

—™™ur—te even for low levels of iwq —™tivityF „he improved ˜eh—viour of this —lgoE

rithmD with just — modest in™re—se in the ™omput—tion—l ™omplexityD ™—n —void the

os™ill—tions of yxEypp timingF „he —im of this elgorithm it w—s to use the simE

plest noise thresholdE˜—sed estim—tion methodD whi™h determine the ˜eginning level
        RT                               RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



of iwq sign—lD —nd to —void the dr—w˜—™k presented ˜y some os™ill—tions of yxEypp

timing in the ˜eginning of iwq sign—l9s —™tiv—tionF



4.3 Filter design
ƒign—l pro™essing ™—n ˜e de(ned —s sign—l m—nipul—tion for either extr—™ting inforE

m—tion or produ™ing —n new represent—tion of this sign—l through —n—lysisF yther

motiv—tions of sign—l pro™essing —re the removing of unw—nted ™omponents ™orruptE

ing the sign—l of interestD whi™h is our study in this se™tion —nd the extr—™ting of

useful inform—tionD whi™h is the go—l of our study in the following se™tions RFRFPD RFRFQ

—nd RFRFRF „his se™tion points on (ltering —nd frequen™y dom—in represent—tion of the

ƒign—lF „he prin™iple fun™tion of — (lterD (gure RFVD is to (lter out the unw—nted p—rts

of —n input sign—lF „he unw—nted frequen™y p—rts of the sign—l —s des™ri˜ed in se™tion




                     pigure RFVX pilter e'e™t on sign—l9s spe™terF


QFQ ™—n not ˜e —ll elimin—tedD ˜ut only redu™edF sn m—ny ™—sesD the sequenti—lly loE

™—lis—tions of the inform—tion ™—rried ˜y the o˜served sign—l —nd the distur˜—n™es —re

gener—lly known a prioriF „he o˜je™tive is then to ˜uild — new sign—l from the r—w

sign—l ˜y ex™lusion of the distur˜—n™esF e digit—l (lter is just — (lter th—t oper—tes on

digit—l sign—ls represented inside — ™omputerF „here —re plenty of softw—res —v—il—˜le
RFQF pilter design                                                          RU



for designing digit—l (ltersF „he e'e™tive use of — (lter design —lgorithm requires —n

underst—nding of its p—r—meters designingD whi™h requires —lso some underst—nding of

(lter theory ‘TR“F piltering is — ™omput—tion whi™h t—kes one sequen™e of num˜ers of

input sign—l —nd produ™es — new sequen™e of num˜ers of (ltered output sign—lF „he

digit—l (lter design methods f—ll into two m—in ™—tegoriesX IA pinite smpulse ‚esponse

@FIR A (lter design —ndD PA sn(nite smpulse ‚esponse @IIR A (lter designF foth these

two types ™—n ˜e designed with —ny st—nd—rd method @ButterworthD ChebeshevD et™FFFAF

smpulse response of — digit—l (lter is the output sequen™e from the (lter when — unit

impulse is —pplied —t its inputF e unit impulse is — simple input sequen™e ™onsisting

of — single v—lue of 1 —t time t = 0D followed ˜y zeros —t —ll su˜sequent s—mpling

inst—ntsF por ps‚ (ltersD the ™urrent output y(n) is ™—l™ul—ted solely from the ™urrent

—nd previous input v—luesX

                          y(n) = x(n), x(n − 1), x(n − 2), ...                   @RFQFIA

„his type of (lter is s—id —lso nonEre™ursiveD ˜e™—use these (lters usu—lly require no

feed˜—™kF sn this ™—se the impulse response of ps‚ (lter is of (nite dur—tionF

„he IIR (lters —re ™ommonly implemented using — feed˜—™k @re™ursiveA stru™tureF „he

word re™ursive me—ns 4running ˜—™k4D —nd refers to the f—™t th—t previouslyE™—l™ul—ted

output v—lues go ˜—™k into the ™—l™ul—tion of the l—test outputF „he expression for —

re™ursive (lter therefore ™ont—ins not only terms of input v—luesX x(n), x(n − 1), x(n −

2), . . .D ˜ut —lso terms of output v—luesX y(n − 1), y(n − 2), . . .F sn this ™—se the

impulse response of IIR (lter is theoreti™—lly not of (nite dur—tion ˜ut ™ontinues for

everF „he re™ursive terms or previous output terms feed ˜—™k energy into the (lter

inputF

qener—llyD to design — given frequen™y response ™h—r—™teristi™D re™ursive (lter requires
        RV                               RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



fewer terms to ˜e ev—lu—ted ˜y the pro™essor th—n the equiv—lent nonEre™ursive (lterF

„he re™ursive system is spe™i(ed ˜y two ve™tors a —nd bF „he ™oe0™ients of ve™tor

b —re ™onvolved with the ™urrent —nd p—st input s—mplesD while a ™oe0™ients —re

™onvolved with the p—st output s—mplesF „o ™—l™ul—te ‘SQ“ output s—mple y(n)D the

(lter multiplies the ™urrent —nd p—st input s—mples x(n), x(n − 1), x(n − 2), x(n −

3), ..., x(n − k) ˜y the set of b ™oe0™ientsX b(0), b(1), b(2), b(3), ..., b(k)Y —nd sums

themD then the (lter multiplies the p—st output s—mplesX y(n − 1), y(n − 2), y(n −

3), ..., y(n − k A ˜y the a ™oe0™ientsX a(1), a(2), a(3), ..., a(k) —nd sums themD then

it ™om˜ines them to form the output y(n)D —™™ording to this equ—tion RFQFPX

                      y(n) =      x(n − i)b(i) −     y(n − i)a(i)                 @RFQFPA

sn MATLAB tool˜oxD this whole pro™ess is performed ˜y the (lter fun™tionX y =

f ilter(b, a, x)F „his fun™tion uses —n in(nite impulse response @IIR A or (nite impulse

response @FIR A (lterY whereX x is the input sign—lD y the output sign—lD —nd where b

—nd a —re the ™oe0™ientsF „he v—lues of these ™oe0™ients determine the ™h—r—™teristi™s

of — p—rti™ul—r (lterF „he order of — digit—l (lter ™—n ˜e de(ned —lso —s the num˜er

of previous inputs @stored in the pro™essor9s memoryA used to ™—l™ul—te the ™urrent

outputF sn the ™—se of re™ursive (ltersD the de(nition ™—n ˜e extended to previous

input —nd output v—lues required to ™ompute the ™urrent outputF

fefore to go f—rther it is prefer—˜le to t—lk —˜out the —li—sing pro˜lemD whi™h h—s ˜een

des™ri˜ed —lre—dy in se™tion QFIF „o prevent —li—sing pro˜lem it is more —dv—nt—geous

to (lter the ™ontinuousEtime sign—lD using —n—log (lters ˜efore s—mpling itD @˜iomedi™—l

—ppli™—tions involve the —™quisition of ™ontinuousEtime sign—lsAF

Matlab tool˜ox h—s sever—l design —lgorithms th—t ™—n ˜e used to ™re—te ˜oth IIR —nd

FIR digit—l (ltersF „he IIR (lters th—t ™—n ˜e ™re—ted in Matlab —re ButterworthD
RFQF pilter design                                                          RW



Chebyshev-1D Chebyshev-2D —nd ellipticF „he FIR (lter —lgorithms in Matlab —re

equirippleD least squaresD —nd Kaiser window typesF ‡e should know the p—r—meters

of the (lter th—t we —re going to designF ƒome of these p—r—meters —re des™ri˜ed in

following se™tionF



4.3.1 Optimised lter design
hesign mode —llows us to spe™ify — FIR or IIR (lter ˜y setting design p—r—meters su™h

—s (lter typeD p—ss˜—ndGstop˜—nd edge frequen™iesD p—ssE˜—nd —nd stopE˜—nd ripple

levelsD —nd stopE˜—nd —ttenu—tionF ‡e ™—n sele™t from design methods th—t in™lude

futterworthD ChebyshevD snverse ChebyshevD EllipticD KaiserD EquirippleD . . . F „he

designer should then use di'erent p—r—meters to suggest — (lter meeting —s m—ny of

those spe™i(™—tions —s possi˜leF „he go—l is then to optimise the designed (lter to meet

desired needsF „he MATLAB sign—l pro™essing tool˜ox ™ont—ins — num˜er of di'erent

fun™tions for designing re™ursive lowEp—ssD highEp—ss —nd ˜—ndEp—ss (ltersF …sing

MatlabD — digit—l (lter is designed with v—rious prototypesX ChebyshevD ButterworthD

—nd Elliptic for IIR typeF EquirippleD least squaresD —nd Kaiser window —re designed

for FIR typeF „he optimum (lter type is ™hosen on the ˜—sis of implement—tion

™omplexity —nd m—gnitude responseF „he design spe™i(™—tions of the ˜—ndEp—ss (lter

—nd the order —re given for the following ex—mplesF e ™omp—rison of these (lters is

—ttempted in this se™tion in order to ev—lu—te the —dv—nt—ges —nd dr—w˜—™ks of e—™h

(lter for the s—me ˜—nd frequen™yD whi™h equ—l to BP a ‘30Hz, 500Hz “F


   1) Innite Impulse Response (IIR) digital lters:
„he futterworth (lterD for sn(nite smpulse ‚esponse (lter design without spe™i(ed

requirementsD is often su0™ientF wore rigorous (lter requirements ™—n ˜e met with
        SH                             RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



Chebyshev —nd elliptic (ltersD (gure RFWF por e—™h type of IIR (lterD three order

v—lues h—ve ˜een ™hosenX PD R —nd TF „hese (lter responses (gure RFW designed with




pigure RFWX sn(nite smpulse ‚esponse @IIR A ˜—ndEp—ss (lters ™omp—rison for orders
n = 2, 4 and 6F


low ordersD whi™h —re PD R —nd T seem to ˜e good —™™ept—˜leF ‡e ™—n ™on™lude th—t

the ellipti™ (lter of order T presents the ˜est ˜—ndEp—ss frequen™y responseD ˜e™—use

its p—ssE˜—nd —nd stopE˜—nd ™uto' frequen™ies tr—nsition —re f—stD in ™omp—rison with

the two othersF


   2) Finite Impulse Response (FIR) digital lters:
FIR (lters require — mu™h higher (lter order th—n IIR (lters to —™hieve — given —lmost

s—me level of perform—n™eF „he MATLAB fun™tion r1 @N, Wn, type of window(N) A

designs ™onvention—l FIR (lters ˜—sed on the windowing methodF ‡ithout expli™it

spe™i(™—tionsD the r—mming window is employed in this designF yther windowing

fun™tions ™—n ˜e used ˜y spe™ifying the windowing fun™tion —s —n extr— —rgument of
RFQF pilter design                                                         SI



the fun™tionF por ex—mpleD Blackman windowD Hanning window or rectangular winE

dowF „he Parks-McClellan method @™—lled 4Remez 4 ˜y Matlab A designs F IR (lter

of order N ˜—sed on Parks-McClellan —lgorithm —nd exhi˜its —n equiripple ˜eh—vior

in their frequen™y responses —nd —re sometimes ™—lled equiripple (ltersF pilter spe™iE

(™—tions —re given in terms of p—ssE˜—nd —nd stopE˜—nd ™uto' frequen™iesD moreover

using —lso p—ssE˜—nd —nd stopE˜—nd ripples —ttenu—tionF ƒome of F IR (lter types

—re presented in (gure RFIHF xote th—t the frequen™y response of F IR (lter ˜—sed on

Parks-McClellan —lgorithmD presented in (gure RFIH h—s — high stopE˜—nd g—inD this

is due to the n—rrow tr—nsition ˜—ndF sf the tr—nsition ˜—nd ˜e™omes l—rger we will

get lower stopE˜—nd g—inF „here is — tr—deEo' ˜etween stopE˜—nd g—in —nd tr—nsition

widthF foth IIR —nd F IR de(nes — ™l—ss of digit—l piltersF IIR (ltersD whi™h m—y




pigure RFIHX pinite smpulse ‚esponse @ps‚A ˜—ndEp—s (lters ™omp—rison for orders
naRHD TH —nd VHF


h—ve ˜oth zeros —nd poles on the zEpl—neD —re not gu—r—nteed to ˜e st—˜leD —nd they
         SP                               RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



h—ve nonline—r ph—se responsesF F IR h—s zeros only on the zEpl—neD the ™onsequen™es

of this —re th—t F IR (lters —re —lw—ys st—˜leD —nd they h—ve line—r ph—se responses

@(lter9s ™oe0™ients —re symmetri™—lAF sn this ™—se the del—y is ™onst—nt for —ll freE

quen™iesF

e simple design spe™i(™—tion for — (lter is to remove noise outside — ™ert—in ˜—ndEp—ss

frequen™yF e more ™omplete spe™i(™—tion need some other spe™i(™ ™h—r—™teristi™s like

p—ssE˜—nd ripple @Rp D in de™i˜elsAD stopE˜—nd —ttenu—tion @Rs D in de™i˜elsAD or tr—nsiE

tion width @Wp D Ws D in hertzAF „hese spe™i(™—tions should —™hieve the perform—n™e

go—ls with the minimum (lter orderF ƒu™h t—sk ™—n ˜e done using the following matlab

fun™tions likeX chebyordD butterordD ellipordD ...F

pilter ƒpe™i(™—tions in Matlab —reX

   • Wp X €—ssE˜—nd ™uto' frequen™ies

   • Ws X ƒtopE˜—nd ™uto' frequen™ies

   • Rp X €—ssE˜—nd rippleX devi—tion from m—ximum g—in @dB A in the p—ssE˜—nd

   • Rs X ƒtopE˜—nd —ttenu—tionX devi—tion from H g—in @dB A in the stopE˜—nd

sn (gure RFIID two ex—mples —re presented to ™omp—re the required order for e—™h type

of (lter for —lmost the s—me spe™i(ed ™h—r—™teristi™sD whi™h —reX stopE˜—nd ™uto' freE

quen™y Ws = [30Hz, 500Hz]D €—ssE˜—nd ™uto' frequen™ies Wp = [40Hz, 400Hz]D

Rp = 2dB @ripple in the p—ssE˜—ndAD Rs = 20dB @—ttenu—tion in the stopE˜—ndA for

IIR Chebychev (lterF gon™erning F IR (lter with Kaiser windowD the p—r—meters

of ve™tor devs = [0.29, 2, 0.29]D spe™ify the p—ssE˜—ndD ripple —nd the stopE˜—nd

—ttenu—tion in —˜solute v—lues —nd not in de™i˜elsF por —lmost s—me (lter ™h—r—™E

teristi™sD F IR with Kaiserwindow required —n order n = 80D ˜ut IIR Chebychev
RFQF pilter design                                                         SQ



(lter h—s required only —n order n = 6F xote th—t the num˜er of (lter ™oe0™ients




pigure RFIIX ‚equired order for ˜oth ps‚ —nd IIR (lters in ™—se of —lmost s—me
™h—r—™teristi™sF


—'e™ts signi(™—ntly on the ™omput—tion—l e'ort needed for the designing of the (lterF

e l—rge num˜er of (lter ™oe0™ients requires l—rger ™omput—tion—l time th—t m—y not

˜e fe—si˜le in ™ert—in re—lEtime —ppli™—tionsF e gener—l desire in —ny (lter design is

th—t the num˜er of oper—tions @—dditions —nd multipli™—tionsA needed to ™ompute the

(lter response is to ˜e —s low —s possi˜leF



4.3.2    FIR-80th and IIR-6th order lter responses for dierent
         window types
„his se™tion de—l with the frequen™y response of —n F IRE80th order —nd IIRE6th order

€—ssE˜—nd (lters ™orresponding to di'erent window typesF ‡e will ™onsider di'erent

window ™h—r—™teristi™s in frequen™y r—nge of 30−200Hz D —nd will ™omp—re the qu—lity

me—sures —nd ™omplexity issues rel—ted with these two design te™hniquesF por IIR

(lter the window types used —reX butterworthD chebychev-1 —nd ellipticD whi™h —re

presented in (gure RFIPF sn (gure RFIQ —re presented the frequen™y responses of

four 80th order F IR (lter ™orresponding to the following four windowsX rectangular
           SR                            RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



windowD hanning windowD Blackman —nd P arks − M cClellanF               „he (lter order




pigure RFIPX prequen™y response of IIRE6th order (lter for three di'erent windowsF


is given ˜y the length of its (lter impulse responseD whi™h ™—n ˜e ™onsidered —s its

me—sure of ™omplexityF elthough IIR (lter design h—s sm—ller order @6th orderAD its

frequen™y response is ™omp—r—˜le with th—t of the 80th order F IR (lterF yn viewpoint

of ™omplexity IIR (lter is prefer—˜leF sn 6th order IIR (lter designD the me—sure of

(lter qu—lity is good enough with —lso less ™omplexityF



4.3.3 Order eect of IIR-elliptic lter
„he investig—tion of the vi—˜ility of myoele™tri™ sign—l re™ognition ˜y di'erent (ltering

pro™esses is ™onsideredF iwq sign—l —n—lysis need (rst the use of lowEp—ss —ntiE

—li—sing —n—logE(lterF „his —ntiE—li—sing —n—logE(lter h—s ™uto' frequen™y somewh—t

—˜ove 500Hz D in this ™—se 900Hz D —nd h—s s—mpling frequen™y —t —lmost four times

the highest frequen™yD in this ™—se 4000Hz F „he digitised iwq sign—l ™—n ˜e then

(lteredF
RFQF pilter design                                                              SS




pigure RFIQX prequen™y response of F IRE80th order (lter for four di'erent windowsF

e v—riety of —˜ove IIREellipti™ (lter were —pplied with di'erent ordersX 2, 4 and 6F

iwq sign—ls ™orresponding to three di'erent (nger movementsD whi™h —re the )exion

of thum˜ED pointerE —nd middleE(nger —re ™onsideredF „hree di'erent fe—tures —re

extr—™ted from these (ltered sign—ls —nd ™l—ssi(ed using RBF intelligent ™l—ssi(™—tion

methodF „hese fe—tures —re woments of frequen™y 9Mn 9 given in equ—tion RFQFQ with

di'erent v—lues of n @orderAD n = 0, 1 and 2F

                     Mn (t) =        n
                                    ωk | ST F T (t, k) |, n = 0, 1, 2, 3, ...        @RFQFQA
                                k

where

Mn X is the nth moment of the frequen™y distri˜ution —t time tD

nX orderD

ω X frequen™yF

„he following (gure RFIRD in ™—se of illipti™ IIR (lter —nd ‚—di—l f—sis pun™tion

@RBF A ™l—ssi(™—tion methodD presents the ™l—ssi(™—tion results of these three (nger

movementsF ‚—di—l f—sis pun™tion @RBF A neur—l network —r™hite™ture is designed
        ST                             RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




   pigure RFIRX i'e™t of IIR (lter orders on iwq sign—l ™l—ssi(™—tion —™™ur—™yF

—nd tr—ined ˜y 4newrb 4 Matlab fun™tion with IT test sets —nd IT tr—ining setsF „he

output l—yer is line—r —nd the r—te of ™l—ssi(™—tion is depending on spre—d v—lues of

hidden unitF ren™e four v—lues of spre—d ˜etween HFR —nd IFT with — step of HFR —re

usedF „he ev—lu—tion of the (lter order e'e™t on iwq sign—l ™l—ssi(™—tion —™™ur—™y

will ˜e ™le—rly presented with these four di'erent spre—d v—lues —nd three di'erent

fe—turesF „he p—ssE˜—nd frequen™y is ™hosen to ˜e in the r—nge of 10 − 500Hz F „hese

results show ™le—rly th—t the in™re—sing of (lter order v—lues h—s — positive e'e™t on

iwq sign—ls ™l—ssi(™—tionF



4.3.4 Eect of dierent lter window types
ell (ltersD F IR —nd IIRD des™ri˜ed in se™tion RFQFI will ˜e used to ™omp—re the

dis™rimin—tion —™™ur—™y ˜etween themD (gure RFISF „he ™hoi™e of (lter type is —n

import—nt de™ision for iwq sign—ls re™ognitionF „he fe—tures —nd the method of
RFQF pilter design                                                         SU




pigure RFISX i'e™t of di'erent window types of 6th order IIR (lter —nd 80th order
F IR (lterD on iwq sign—l ™l—ssi(™—tion —™™ur—™yF

™l—ssi(™—tion used in this p—rt —re the s—me with those given in —˜ove se™tion RFQFTD

—nd —re illustr—ted in (gure RFIRF „he orders of IIR —nd F IR (lters —re sele™ted with

™onsider—tion of the ˜est results found in —˜ove studyD se™tion RFQFID (gures RFW —nd

RFIHAF „hese —ll (lters —re tested on re—l iwq sign—l me—surements of three di'erent

(nger movementsF RBF ™l—ssi(™—tion method is used to ev—lu—te the e'e™t of the

window type for ˜oth 80th order F IR (lter —nd 6th order IIR (lter designF



4.3.5 Pass-band eect of IIR-elliptic lter
pilters pl—y — vit—l role in d—t— —™quisition —nd pro™essing systems to remove unw—nted

sele™ted frequen™ies from —n in™oming iwq sign—l —nd minimise —rtif—™tsD ™ondu™ted
        SV                             RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



distur˜—n™es —nd emitted distur˜—n™esF iwq sign—l o'ers — gre—t de—l of useful inE

form—tionD whi™h is depending on its ˜—nd frequen™yF por some fe—turesD like moment

of se™ond order @M2 A illustr—ted in this following ex—mple given in (gure RFITD the

™hoi™e of the €—ssE˜—nd (lter is very import—nt in viewpoint of its inform—tionF „his




 pigure RFITX i'e™t of IIR-elliptic (lter9s €—ssE˜—nd on iwq sign—l ™l—ssi(™—tionF


inform—tion depends on (lter frequen™y p—ssE˜—ndF „he (gure RFIT shows ™le—rly th—t

the di'erent p—ssE˜—nd widths h—ve —n in)uen™e on the ™l—ssi(™—tion —™™ur—™yF es

ex—mple three (nger movements @thum˜ED pointerE —nd middleE(ngerA —re ™onsideredF

pive p—ssE˜—nds —re ™hosenD whi™h —reX 3-800HzD 10-500HzD 20-400HzD 30-300HzD 50-

200HzF gl—ssi(™—tion method used here is ‚—di—l f—sis pun™tion @RBF A methodD

whi™h ™onsiders four spre—d v—luesX 0.4, 0.8, 1.2 —nd 1.6F „he ˜est ™l—ssi(™—tion reE

sults —re o˜t—ined with p—ssE˜—nd equ—l to 10-500HzF st is ne™ess—ry here to give this

following import—nt rem—rkF „his optimised p—ssE˜—nd found for used fe—ture @M2 A
RFQF pilter design                                                           SW



™—n not ˜e gener—lised for —ll other fe—turesF wore det—ils —˜out this o˜serv—tion —nd

its —pprovement is given in

   ™h—pter UD se™tion UFPF



4.3.6 Conclusion
„he sign—ls in — digit—l (lter —re represented ˜y (nite —nd qu—ntised ˜in—ry v—luesF

sn this se™tion sever—l (lter ordersD (lter typesD windows —nd (lter p—ssE˜—nds were

designedD tested —nd ™omp—red to ev—lu—te their e'e™t on —n ele™troEmyogr—m sign—l

re™ognitionF „hese systems —re gener—lly used to perform — (ltering oper—tionF st

is import—nt to ev—lu—te the e'e™t of these di'erent (ltering methods on the iwq

sign—l re™ognition to ˜e —˜le to ™hoose the optim—l oneF

„he ™ost of the (lter is determined ˜y its ™omplexityF „his ™omplexity ™—n ˜e ev—lE

u—ted on the ˜—sis of the following four simple p—r—metersX orderD —dder oper—tionsD

multiplier oper—tions —nd del—ysD ‘PQ“F sf only orderEp—r—meter is ™onsideredD the

™l—ssi(™—tion results o™™urred with RBF ™l—ssi(™—tion methodD (gure RFIS —re —lmost

the s—me for these ˜oth (lters@IIR (ltersD whi™h h—ve order = 6D —nd F IR (ltersD

whi™h h—ve order = 80AF st is possi˜le here to ™on™lude th—t IIR (lters —re less ™omE

plex —nd le—d to the s—me —™™ur—™y ™l—ssi(™—tion results th—n F IR (ltersD whi™h —re

more ™omplexF e˜out the ™hoi™e of p—ssE˜—nd (lterD whi™h h—ve — gre—t import—n™e to

tr—nsmit — wellEde(ned inform—tion —nd to reje™t other distur˜—n™esD it is for us now

not possi˜le to ™on(rm if the p—ssE˜—nd (lter 10-500 HzD found in —˜ove se™tion —s

˜est one for the fe—ture M 2D ™—n ˜e gener—lised for —ll other fe—turesF st will ˜e shown

in se™tion U th—t the des™ri˜ed inform—tion inside the s—me sign—l through di'erent

fe—tures is not lo™—ted in the s—me frequen™y ˜—nds of this sign—lF pin—lly six di'erent
        TH                                RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



fe—turesD three of them ˜elong to 6th order IIR (lter —nd three others ˜elong to 80th

order F IR (lterD —re ev—lu—ted —nd ™omp—red to get their ™l—ssi(™—tion e'e™tsF wost

of these (lters h—ve —lmost the s—me results for fe—ture M 2 —nd for frequen™y ˜—nd

in the r—nge of 10-500HzF



4.4 Signal analysis and feature extraction

4.4.1 Introduction
ƒign—l represent—tion is very import—nt ˜efore to de—l with fe—tures extr—™tionF „here

—re three known di'erent represent—tions of — sign—lX IA timeEdom—inD PA frequen™yE

dom—in —nd QA timeEfrequen™y dom—in represent—tionF

„he (rst study will ˜e fo™used on fe—tures extr—™tion in time dom—inD then we use

the frequen™y dom—in —nd (n—lly timeEfrequen™y dom—in is ™onsideredF iwq sign—l

is — very ™omplex sign—lF qener—lly — sign—l is — ™—rrier of inform—tionD whi™h ™—n ˜e

represented —s — fun™tion of v—ri—˜lesF


                                  Signal = f (x, y, ).                           @RFRFIA


ƒign—lsD eFgF —n ile™tromyogr—ph @iwqAD —re sign—ls of ™omplex physi™—l phenomen—

v—rying in the timeX

                                 Signal = f (t; x, y, ).                         @RFRFPA

„he iwq —™tivity represents the sum of potenti—ls of —ll —™tive motor unit —™tionsD

(gure RFIUD under the deriv—tive —re— of the ele™trodesF por the —n—lysis of these re—l

—nd ™omplex iwq sign—lsD spe™i—l methods of —n—lysis —re ne™ess—ryD whi™h —llow

the ex—min—tion of the import—nt inform—tion v—ri—˜ility in the tempor—l ™h—nge of
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                TI




                       pigure RFIUX e™tive motor unit —™tions


— fe—ture 4x4F „here˜y it is possi˜le to ˜uild sever—l ™lusters reg—rding to ™lusters

inform—tion di'eren™esF „he —™™ept—˜le fe—tures o˜t—ined using ™ert—in extr—™tion

methods from — sign—lD whi™h ˜elongs to one ™—tegoryD should h—ve the following

™h—r—™teristi™sX


   • they h—ve strong dis™rimin—ting ™—p—˜ilities


   • they —re ro˜ust —nd reli—˜le


   • they —re not time ™onsumm—ting


   • they don9t h—ve m—ny p—r—meters


„his set of —ttri˜utes is ™—lled — sign—ture for the —sso™i—ted sign—lF „his sign—ture

™—n then ˜e used to dete™t the presen™e of simil—r —ttri˜utes in unknown d—t—F ƒin™e

the iwq sign—ls —re nonEst—tion—ry these sign—tures will ˜e extr—™ted using — „imeE

frequen™y —n—lysis of the sign—lsD like ƒhort „ime pourier „r—nsform @ST F T AF frie)yD

in this ™h—pter we w—nt to —nswer these two following questionsX
        TP                              RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



IA ‡hi™h —n—lysis methods —re suit—˜le to use for extr—™tion of the useful fe—turesc E

PA ‡hi™h fe—tures —re the ˜est for the dis™rimin—tion of di'erent mus™le dyn—mi™sc



4.4.2 Time domain feature extraction
‡e w—nt to test the di'erent known forms of iwq sign—l represent—tions th—t —re

more e0™ient for fe—ture extr—™tionF „here —re three known represent—tions for e—™h

time v—rying sign—lX

    • emplitude vsF time represent—tion @Ph dimension—l sp—™eAF

    • emplitude vsF frequen™y represent—tion @Ph dimension—l sp—™eAF

    • „imeEprequen™y vsF emplitude represent—tion @Qh dimension—l sp—™eAF

„he pro™ess ˜egins with re—ding the iwq sign—ls from two surf—™e ele™trode ™h—nnels

—tt—™hed to the test su˜je™t9s fore—rmF „he tr—nsient p—rt @the ˜eginning p—rtA of

iwq sign—l during 400 ms h—s ˜een exploited to extr—™t time dom—in fe—tures for

the re™ognition of R movement ™l—ssesF „hese ™l—sses —reX Q (nger )exion movements

—nd h—nd ™losingF „hese movements were identi(ed when the sign—l9s envelope ™rosses

the noise threshold level @see se™tion RFPD whi™h represents the ™onsidered noise level

referen™eF „he used sign—l ™—n ˜e extr—™ted from e—™h initi—l p—rt of sign—lD whi™h

needs to ˜e done syn™hronously from ˜oth ™h—nnelsF yn™e the required p—rt of the

wyoele™tri™ sign—l is o˜t—inedD m—ny time dom—in fe—tures of sign—l ™—n ˜e extr—™ted

likeX

    • we—n —˜solute v—lue @MAV AD

    • †—ri—n™e @VAR AD
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                               TQ



   • ‡—veform length @WLAD


   • ‚oot me—n squ—re@‚wƒAF


‡e t—ke in ™onsider—tion only one fe—tureD me—n —˜solute v—lue @MAV AD —s ex—mple

to show the distri˜ution of these fe—ture inst—n™esF „wo (gures —re presented for

r—w sign—lD (gure RFIVD —nd (ltered sign—l in 20-250HzD (gure RFIWF „he v—lues —re

norm—lised to get me—n v—lue equ—l zero —nd v—ri—n™e v—lue equ—l to oneF        „his




   pigure RFIVX we—n —˜solute v—lue inst—n™es distri˜ution with r—w iwq sign—l


ex—mple shows us th—t the fe—tures extr—™ted simplyD from r—w —nd (ltered iwq

sign—l in time dom—in present—tionD without —ny sign—l —n—lysis —re not relev—ntF „he

four ™l—sses —re not regrouped in dis™rimin—ted ™lustersD hen™e we ™—n9t di'erenti—te

˜etween themF „empor—l —ppro—™h ™—n not extr—™t import—nt inform—tion for the

™l—ssi(™—tion of these four di0™ult g—sp typesD espe™i—lly with only two me—surement

™h—nnelsF
        TR                               RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




pigure RFIWX we—n e˜solute v—lue inst—n™es distri˜ution with (ltered iwq sign—lD
20 − 250Hz F

4.4.3 Frequency domain feature extraction
a) Frequency domain analysis:

„he frequen™y dom—in is used to extr—™t inform—tion ™ont—ined in iwq sign—lF „he

tr—nsform—tion from time dom—in to frequen™y dom—in ‘RT“ is —™hieved through the

use of the pourier tr—nsformD whi™h —llows us to look —t iwq sign—l energy —s —

fun™tion of frequen™yF pourier „r—nsform method is —n optim—l solution when we

—ssume th—t there is no frequen™y ™h—ngeD for e—™h ™omponentD over entire time of

en—lysisF ƒu™h —n—lysis does not t—ke in ™onsider—tion the inform—tion on — time

lo™—lis—tion of the frequen™y ™omponent of the sign—lF „he pourier „r—nsform @F T A

is de(ned in equ—tion RFRFQX
                                          +∞
                               X(f ) =         x(t)e−j2πf t                     @RFRFQA
                                         −∞

X(f ) is — ™omplex fun™tion of frequen™yD f D whi™h des™ri˜es the ™omplex volt—ges

@—mplitudes —nd ph—sesA —s — fun™tion of frequen™yD f D of the sign—l x(t)F
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                 TS



The Discrete Fourier Transform (DF T ):

sf x(t) is timeEfun™tion limited to — dur—tion of nT s—mples then DF T D equ—tion RFRFRD

™—n ™onvert — s—mpled fun™tion of time x(nT ) into — s—mpled fun™tion of frequen™y

X(mF )F sn simple terms we use the DF T to represent digit—l sign—lD x(nT )D of length

nT —s — sum of m di'erent sinusoid—l w—veformsF sn these sinusoid—l w—veforms e—™h

sinusoid—l fun™tion @™omplex exponenti—l fun™tionA X(mF )D will h—ve only one single

frequen™y —mplitude —nd ph—seF

                             X(mF ) =        x(nT )e−jnm2π                       @RFRFRA
                                         n

„he p—st pourier „r—nsform @F F T A is — ™l—ss of —lgorithmD whi™h de—ls only with

time ™omput—tion redu™tionF st —llows the ™omput—tion of the DF T to ˜e performed

in y@x log xA r—ther th—n y@N 2 A ™omput—tionsF „he DF T of iwq sign—l produ™ed

with thum˜E(nger )exion during 400ms —nd s—mpled —t Fs = 4Khz D is presented in

(gure RFPH




pigure RFPHX pourier „r—nsform @F T A —n—lysis of r—w iwq sign—l of 400ms lengthD
™orresponding to thum˜ (nger )exion movementF
           TT                            RFH   ƒign—l pro™essing —nd fe—ture extr—™tion



b) sinusoidal harmonic waves

„he DF T is used to model our iwq sign—l —s — sum of simple sinusoid—l sign—lsF „he

m—gnitudes of spe™tr—l lines of these simple sinusoid—l sign—ls qu—ntify their energy

™ontri˜ution for the glo˜—l iwq sign—lF rowever iwq sign—ls —re mu™h more ™omE

plex th—n simple sinusoid—l fun™tionsF por — sign—l x(nT )D whi™h ™ont—ins nT d—t—

s—mplesD the DF T in this ™—se is resulted in nT dis™rete h—rmoni™—lly rel—ted sinuE

soidsF „he spe™tr—l lines will ˜e o™™urred —t the fund—ment—l frequen™y th—t equ—l to
FS
nT
   F   „his fund—ment—l frequen™y ™—n ˜e used to get —ll de™omposed sign—l frequen™ies

of our origin—l sign—l x(nT )F sn the following (gure RFPI we present 8 sinusoid—l deE

™omposed sign—lsF „hese sign—ls —re ™ont—ined in — ˜—nd of frequen™y ˜etween 2.5Hz

—nd 2400Hz D of iwq sign—l —™™ording to thum˜ (nger )exion re™orded during 400ms

—nd s—mpled —t Fs equ—l to 4kHz F i—™h sign—l of (gure RFPI is — ™om˜in—tion of 12 eleE




pigure RFPIX r—nd ™losing ‚—w iwq sign—l de™ompositionD in 8 group sign—lsF i—™h
of them is ™omposed of 12 spe™tr—l lines issued from DF T —n—lysis methodF


ment—ry sinusoid—l de™omposed DF T 9s sign—lsD —nd its frequen™y is the —ver—ge v—lue
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                TU



of their frequen™iesD —nd its —mplitude is — sum of their —mplitudesF ever—ge frequenE

™ies for these 8 sign—ls —reX 15Hz, 45.5HZ, 75Hz, 105Hz, 135Hz, 165Hz, 195Hz

—nd 225Hz F „he dom—in frequen™y ™overed ˜y e—™h spe™tr—l line is equ—l to 2.5Hz F

‡e use this represent—tion of the iwq sign—lD whi™h is frequen™yEdom—in —n—lysis

to knowD through extr—™tion of ™orrespondent fe—turesD if there is —melior—tion in

dis™rimin—tion ™l—ssesF „he ™h—nges in the spe™trum of iwq sign—l h—ve ˜een used

—s —n o˜je™tive me—surement of mus™le dyn—mi™sF „he used sign—l ™—n ˜e extr—™ted

from initi—l p—rtD whi™h needs to ˜e done syn™hronously from two ™h—nnelsF yn™e the

required initi—l p—rt of the wyoele™tri™ sign—l is o˜t—inedD m—ny frequen™yEdom—in

fe—turesD whi™h —re known in the liter—tureD ™—n ˜e extr—™ted likeX

   • wedi—n frequen™y

   • we—n frequen™y



c) Frequency domain feature extraction


1- Median frequency:

‡e —ttempt to improve the dis™rimin—tion ™—p—˜ility for our four ™l—sses using fe—tures

rel—ted to dom—in frequen™y represent—tionF yne me—sure of the frequen™y ™ontent in

— sign—l is the medi—n frequen™yF st9s the me—sure of the iwq sign—l frequen™y th—t

divides the sign—l into two h—lves of equ—l powerF „he fe—ture s—mples —re presented

in two dimension—l fe—ture sp—™e @2DA de(ned with two me—sure ™h—nnelsD (gure RFPP



   2- Mean frequency X

„he se™ond me—sure of the frequen™y ™ontent in — sign—l is the me—n frequen™yF „he
        TV                             RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




pigure RFPPX wedi—n frequen™y fe—ture inst—n™es distri˜ution ™orresponding to
frequen™yEdom—in iwq sign—l represent—tionF


me—n frequen™yD equ—tion RFRFSD ™—n ˜e determined from the F F T —sX


                                                           fi Ai 2
                       M eanF requencyF eature =       i
                                                                2 ,            @RFRFSA
                                                           i Ai




„hese fe—ture v—lues —re presented in two dimension—l fe—ture sp—™e de(ned with

two me—surement ™h—nnelsD (gure RFPQF glusters dis™rimin—tion with this fe—tureD

me—n frequen™yD is more ™le—r th—n with medi—n frequen™yF sn (gure RFPQ it ™—n ˜e

™le—rly distingued the pointer (nger ™l—ss represented with ™ir™lesF „he se™ond ™l—ssD

whi™h is less dis™rimin—ted is r—nd ™losing th—t is represented with st—rsF fetween

thum˜ (nger ™luster —nd middle (nger ™luster there is — ˜ig interferen™eF „his se™ond

me—sureD me—n frequen™yD h—s more dis™rimin—tion —™™ur—™y th—n medi—n frequen™yF

RemarkX
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                TW




pigure RFPQX we—n frequen™y fe—ture inst—n™es distri˜ution ™orresponding to
frequen™yEdom—in iwq sign—l represent—tionF


e new me—nEfrequen™y fe—ture ™—n ˜e de(ned in the following equ—tion RFRFTX

                                                            fi Ai
                        M eanF requencyF eature =       i
                                                                  ,             @RFRFTA
                                                            i Ai


where Ai is the F F T —mplitude —t frequen™y fi F „he Ai v—lues —re not squ—red like in

the —˜ove ex—mpleF sn this ™—se we get the following distri˜ution of fe—ture s—mplesD

(gure RFPRX sf we ™omp—re this distri˜ution with the —˜ove one in (gure RFPQD the

dis™rimin—tion —™™ur—™y ˜e™—me worseF


   3- Norm of power density X

e new fe—ture in the frequen™y dom—in is de(nedD whi™h is the spe™trum9s norm

@Norm-Spctr A of the sign—l iwqF „he spe™trum9s norm ™—n ˜e determined —sX


                                             (Ai 2 )                            @RFRFUA
                                         i
        UH                               RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




pigure RFPRX we—n frequen™y fe—ture inst—n™es distri˜ution ™orresponding to
frequen™yEdom—in iwq sign—l represent—tionF

where Ai is the ƒpe™trum —mplitude —t frequen™y fi D —nd the summ—tions —re token

over —ll frequen™ies in the spe™trumF

€ower spe™trum estim—tes the €ower ƒpe™tr—l hensity of the sign—l iwq using

W elch9s —ver—ged periodogr—m methodD (gure RFPS es it is shown in (gure RFPTD

our investig—tions in frequen™y dom—in for relev—nt fe—tures h—ve le—d to —n improved

™lusters dis™rimin—tion of our four ™l—ssesF
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                            UI




   pigure RFPSX ‚—w iwq sign—l of 400ms length —nd its spe™tr—l power densityF




pigure RFPTX xorm of power density fe—ture inst—n™es distri˜ution ™orresponding to
frequen™yEdom—in iwq sign—l represent—tionF
         UP                               RFH    ƒign—l pro™essing —nd fe—ture extr—™tion



4.4.4 Time-frequency domain feature extraction
a) Time-frequency domain analysis

wonoEdimension—l sign—l —n—lysis seems not to ˜e su0™ient for extr—™tion of relev—nt

inform—tion to ™h—r—™terise sign—ls of ™omplex systems like iwq sign—lsF „herefor

we h—ve to ™onsider ˜iEdimension—lD time —nd frequen™yD —n—lysis methodsF „imeE

frequen™y represent—tion ™om˜ines time dom—in —nd frequen™y dom—in —n—lysis to

get tempor—l lo™—lis—tions of — sign—l9s spe™trumF „he ƒhort „ime pourier „r—nsform

@ST F T A ™onsiders th—t the st—tisti™—l properties of the nonEst—tion—ry sign—l —re v—ryE

ing in the timeF „his method of —n—lysis help to extr—™t the inform—tion —™™ording to

the sign—l time v—ri—tionF „he ™hoi™e of timeEwindow to tr—™k these v—ri—tions of the

sign—l is of gre—t import—n™eF

„his p—rti™ul—r pourierE˜—sed —n—lysed methodD ST F T D designs smooth time winE

dows Wi (t) : i = 1, .., pD (gure RFPUD to ™hop — given sign—l into short p pie™es —nd

then —pplying the DF T to e—™h pie™eF ƒin™e we use — sign—l of nT v—lues lengthD

we h—ve to ™onsider th—t p ≤ nF ‡e ™—n9t simply shop the sign—l into short pie™esD

without smooth fun™tionsD ˜e™—use this will ™—use sh—rp dis™ontinuities ˜etween these

se™tionsF ren™e the smooth windowing is ™onstru™ted ˜y multiplying the sign—l xnT

˜y the timeEwindow Wi (t)F

pX num˜er of windowsD —nd Wi (t)X short time —n—lysis window


                             Xi (mF ) =         xi (nT )e−jnm2π                    @RFRFVA
                                          n

„he e—siest w—y to ˜e sure th—t there is ™ontinuity ˜etween ends of these pie™es of

sign—ls is to for™e them to ˜e zero —t the extremitiesD thus their v—lues is ne™ess—rily

the s—meF „he ™hoi™e —mong m—ny existent window fun™tions depends on knowledge
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                 UQ




pigure RFPUX en ex—mple of how the iwq sign—l is windowed to ™re—te — new sign—l
with smoothed extremitiesF



of the sign—l —nd —ppli™—tionF xow it is possi˜le to —pply DF T on e—™h timeEwindowed

sign—lD (gure RFPVF

 efter summ—tion of —ll pourier tr—nsformed sign—ls Xi (mF )Y where i = 1, . . ., pY

we get —s ™onsequen™e result the ƒhort „ime pourier „r—nsform of our origin—l sign—l

x(t)F „hus the ST F T ™onsiders the sign—l x(t) —s — series of DF T s of timeEwindowed

pie™esF st rem—ins some questions —˜out how to ™hoose the timeEwindow length —nd

the r—te of timeEwindows overl—ppingD whi™h depend on the —ppli™—tionF

xow it9s possi˜le to identify how the frequen™y ™ontent of the sign—l evolves over timeF

en —n—lysed p—rt of r—nd ™losing iwq sign—l during 400ms —nd for 25ms timeE

window lengthD using ST F T method represent—tionD ™—n ˜e shown in the following

(gure RFPWF ‡e get the following present—tion of mus™le —™tiv—tionX
        UR                           RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




pigure RFPVX pourier „r—nsform for — windowed iwq sign—l ™orresponding to thum˜
(nger )exionF




pigure RFPWX ST F T —n—lysis of 400ms length iwq sign—l —nd for 25ms time window
lengthD ™orresponding to h—nd ™losing movement using ™ontour present—tionF
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                US



b) sinusoidal harmonic waves

sf the digit—l sign—lD x(nT )D of length nT is representedD using DF T D @—s — sum of

m di'erent sinusoid—l w—veformsAD these sinusoid—l w—veforms h—ve only one single

frequen™y ™omponent independently of timeF rowever with ST F T tr—nsform the

—mplitudes of these spe™tr—l lines —re not ™onst—ntF por the s—me sign—l in (gure RFPW

the spe™tr—l lines —re presented in the following (gure RFQHF i—™h sign—l of (gure RFQH




pigure RFQHX r—nd ™losing ‚—w iwq sign—l de™omposition in 8 group sign—lsF i—™h
of them is ™omposed of 12 spe™tr—l lines issued from ST F T —n—lysis methodF ƒign—l
length is equ—l to 400ms —nd s—mpling frequen™y equ—l to 4KHz F



is ™omposed of 12 element—ry spe™tr—l lines o˜t—ined from ST F T 9s sign—l —n—lysisF

widdle frequen™ies for these 8 sign—ls —reX

15Hz, 45.5HZ, 75Hz, 105Hz, 135Hz, 165Hz, 195Hz —nd 225Hz F
          UT                              RFH    ƒign—l pro™essing —nd fe—ture extr—™tion



c) Feature extraction

efter timeEdom—in —nd frequen™yEdom—in fe—tures extr—™tionD we w—nt to improve

more the ™lusters dis™rimin—tion of the four ™l—sses of h—nd movements des™ri˜ed

—˜ove using timeEfrequen™y dom—in fe—tures extr—™tionF iwq sign—l preEpro™essing

oper—tion using spe™trum —n—lysis ˜—sed on ƒhortE„ime pourier „r—nsform @ST F T A

is —ppliedF „his —n—lysis is — form of lo™—l pourier —n—lysis th—t tre—ts time —nd

frequen™y simult—neouslyF st is possi˜le to exploit —nd to qu—ntify the ˜eh—viour of

dyn—mi™ @non line—r —nd time v—ryingA inform—tion present in these iwq sign—ls —nd

to design dis™rete ™h—r—™teristi™ ve™torsF „hese dis™rete ™h—r—™teristi™ ve™tors ™—n

perform some relev—nt fe—tures th—tD m—y ˜eD le—d to high —nd —™™ur—te ™l—ssi(™—tion

r—tes of these di'erent movement ™l—ssesF „he ˜—si™ spe™tr—l p—r—metersD moment—ry

power —nd moment—ry frequen™yD —re used —s fe—tures ‘PT“F „he extr—™ted fe—tures —reX

IA ™entr—l frequen™y 9Cent.f req 9D PA st—nd—rd devi—tion 9Std.dev 9 —nd QA moments of

frequen™y 9Mn 9F „he de(nition of e—™h fe—ture is given in equ—tions RFRFWD RFRFIH —nd

RFRFIIF

                   Mn (t) =        n
                                  ωk | ST F T (t, k) |, n = 0, 1, 2, 3, ...       @RFRFWA
                              k

                                                    M1
                                    Cent.f req =                                 @RFRFIHA
                                                    M0
                                                M2    M1 2
                              Std.dev =            −(    )                       @RFRFIIA
                                                M0    M0
whereX Mn X is the nth moment of the frequen™y distri˜ution —t time tD nX orderD —nd

ω X frequen™yF

‡ith two ™h—nnels of me—surementD 34 r—w iwq sign—ls —re re™orded for e—™h moveE

ment ™l—ssF „he four ™l—ssesD l—˜eled 1, 2, 3 and 4D give 136 fe—ture s—mplesF „he

distri˜ution of —ll these fe—ture s—mples in two dimension—l @PhA sp—™eD channel1
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                UU




                   pigure RFQIX †—ri—n™eEfrequen™y fe—ture distri˜utionF

—nd channel2 D for these three following fe—turesX IA v—ri—n™e frequen™yD PA ™entr—l

frequen™y —nd QA se™ond order womentD —re shown respe™tively in (gures RFQID RFQP

—nd RFQQF pin—lly we re—™h our go—lD th—t to (nd iwq sign—l represent—tionD whi™h

gives ˜est ™lusters dis™rimin—tion ˜etween these four movement ™l—ssesF prom these

three fe—ture distri˜utionsD presented in (gures RFQID RFQP —nd RFQQD it9s possi˜le to

o˜serveD visu—llyD th—t the groups —re ˜etter sep—r—ted th—n with those extr—™ted from

the two pre™edent iwq sign—l represent—tionsX timeEdom—in —nd frequen™yEdom—in

represent—tionsF
UV                           RFH   ƒign—l pro™essing —nd fe—ture extr—™tion




       pigure RFQPX gentr—lEfrequen™y fe—ture distri˜ution




pigure RFQQX fe—ture distri˜ution of se™ond order frequen™yEmoment
                                  F
RFRF ƒign—l —n—lysis —nd fe—ture extr—™tion                                 UW



4.4.5 Conclusion
„his se™tion is fo™used on me™h—nisms —nd iwqEsign—l —n—lysis methods in order to

produ™e dis™rete ™h—r—™teristi™s @fe—turesAD whi™h ™—n re™ognise di'erent h—nd —nd (nE

ger movement ™l—ssesF „hese di'erent fe—tures extr—™ted with help of di'erent —n—lysis

methodsD —re more or less dis™rimin—tiveF sn this study three di'erent —n—lysis methE

ods —re usedX IA timeEdom—inD PA frequen™yEdom—in —nd QA timeEfrequen™yEdom—inF

„he go—l w—s to extr—™t fe—tures ™orresponding to e—™h —n—lysis method —nd to ™omE

p—re ˜etween their ™lusters dis™rimin—tionF f—sed on only visu—l distri˜ution of these

di'erent fe—ture ™lusters it w—s possi˜le to ™omp—re the level of dis™rimin—tion ˜etween

them —nd to sele™t the ˜est —n—lysis methods —nd ™onsequently ˜est fe—turesF es reE

sults it w—s found th—t the fe—tures extr—™ted from timeEfrequen™yEdom—in —n—lysis

method were more dis™rimin—tive th—n for those two other methodsF
VH   RFH   ƒign—l pro™essing —nd fe—ture extr—™tion
Chapter 5
Feature input space reduction

5.1 Introduction
himension redu™tion ™—n ˜e used for di'erent purposesD in our ™—seD it is used for

™l—ssi(™—tion pro˜lemF „here —re line—r redu™tion methods —nd non line—r redu™tion

methodsF vine—r methods like €rin™iple gomponents en—lysisD whi™h is used in this

™h—pterD is more interpret—˜le th—n non line—r methodsD whi™h ™—n de—l with ™ompliE

™—ted stru™turesF „he role of dimension—lity redu™tion is to simplify highEdimension—l

d—t— sets to ret—in inform—tionD th—t is import—nt for ™l—sses dis™rimin—tionD —nd

dis™—rd th—t whi™h —re irrelev—ntF himension redu™tion methods present sever—l —dE

v—nt—ges likeX


   • possi˜ility to visu—lise fe—ture d—t— in lowEdimension—l sp—™eF


   • produ™e un™orrel—ted new fe—turesF


   • —llow ˜uilding simple modelling orG—nd ™l—ssi(™—tion modelsF


   • redu™e sp—™e ™omplexityF

                                          VI
        VP                                        SFH   pe—ture input sp—™e redu™tion



„he e'e™tive w—y of redu™ing the timeE™onsuming of ™—l™ul—tion is to redu™e or to use

—s sm—ll —s possi˜le the num˜er of fe—ture ve™torsF „he go—l of this ™h—pter is (rst

to present e0™ient method th—t ™—n tr—nsform — given d—t— set X of dimension m to

—n —ltern—tive d—t— set Y of sm—ller dimension pF ƒe™ondly it will ˜e dis™ussed if it9s

ne™ess—ry to use —lw—ys su™h methods for solving ™l—ssi(™—tion pro˜lems or there is

—nother —ltern—tiveF



5.2 Projection method
P CA is — w—y of expressing — high dimension—l d—t— set in —n —ltern—tive set of low

dimension—l d—t— set with high v—ri—˜ilityD whi™h is used for d—t— visu—lis—tion —nd

™lusteringF sn this study — line—r dimension redu™tion te™hnique @P CAAD origin—lly

introdu™ed ˜y uF €e—rson in IWHP see —lso ‘QQ“D is investig—tedF w—ny pro˜lems

in inform—tion pro™essing involve some form of dimension—lity redu™tionF €opul—r

method of dimension—lity redu™tionD P CAD is —n eigenve™tor method designed to

model line—r v—ri—˜ility in high dimension—l d—t— sp—™eF st ™onsiders the gre—test

v—ri—n™eD iFeF get — m—ximum v—lue of the qu—ntityX      i   (xi − xmean )2 D for the eigenE

ve™tors of the d—t— ™ov—ri—n™e m—trixF „his redu™tion is —™hieved ˜y t—king m ve™tors

X1 , X2 , . . . , Xm —nd (nding ™om˜in—tions of them to produ™e prin™ip—l ™ompoE

nentsX P C1 , P C2 , . . . , P Cp D whi™h —re un™orrel—tedY where       p < mF €rin™iple

gomponents @P CsA —re ordered so th—t P C1 exhi˜its the gre—test —mount of the

v—ri—tionD then P C2 exhi˜its the se™ond gre—test —mount of the v—ri—tionD —nd so onF

yn™e eigenve™tors —re found from the ™ov—ri—n™e m—trixD the next step is to order

them following the v—lues9 order of their eigenv—luesD from the highest to lowestF „his

gives us the prin™ip—l ™omponents in order of signi(™—n™eF qener—lly it is written in
SFQF PCA illustr—tion                                                        VQ



the liter—ture th—t this tr—nsform—tion le—ds to — more dis™rimin—ted represent—tion

of d—t—F sn this study it will ˜e shown th—t for relev—nt fe—ture ve™tors this pro™edure

m—y le—d to less dis™rimin—ted represent—tion of d—t— set distri˜utionF st would ˜e

™on™luded —lso th—t there isD some timesD — loss of inform—tion in using dimension—l

redu™tion of d—t— sp—™e for relev—nt fe—turesF


5.3     PCA       illustration
pollowing is — det—iled des™ription of P CA using the ™ov—ri—n™e methodD whi™h proE

vides us the expl—n—tion of P CA —lgorithm —t e—™h stepF „o present this tutori—l

in det—ils —nd gr—phi™—llyD —n ex—mple of two dimension—l sp—™e is proposedF „wo

iwq surf—™e ele™trodes —re pl—™ed on two mus™le groupsD p—ln—ris longus channel1

—nd extensor digitorum channel2 F „he lo™—tion of ele™trodes on the su˜je™t9s —rm is

given in (gure SFIF „wo fe—ture ve™tors Vhc1 —nd Vhc2 for zero order moment @M 0AD —re




  pigure SFIX surf—™e ele™trodes posisition for fore—rm iwq sign—ls me—surements


™onsideredF Vhc1 is fe—ture †e™tor of QR v—ri—˜lesD SFQFID for h—nd ™losing of channel1 D

—nd Vhc2 is fe—ture ve™tor of QR v—ri—˜lesD SFQFPD for h—nd ™losing of channel2 F

                                 T
                               Vhc1 = x1 , x2 , . . ., x34 .                        @SFQFIA

                                  T
                                Vhc2 = y1 , y2 , . . ., y34 .                       @SFQFPA
           VR                                     SFH   pe—ture input sp—™e redu™tion



where T X denotes tr—nsposeF



sn (gure SFP some of QR movements —re presented —s iwq —™tiv—tion for ˜oth ™h—nE

nelsF „he distri˜ution of fe—ture ve™tors of M 0 for r—w iwq sign—l in Ph dimension—l




pigure SFPX some of QR mus™les9 —™tiv—tion of h—nd ™losing with two ™h—nnels iwq
sign—ls me—surements


sp—™e is presented in (gure SFQD see ™h—pter R se™tion RFR —˜out the de(nition of this

fe—tureF



5.3.1 Algorithm's steps illustration
„he steps for ™omputing me—n v—luesD ™ov—ri—n™e m—trixD eigenve™tors —nd eigenv—lues

‘QH“ require the use of — ™omputerE˜—sed —lgorithmsF „hese —lgorithms —re —v—il—˜le

in m—trix —lge˜r— systems —nd —lso in MatLabF


   Step 1: Normalisation
SFQF PCA illustr—tion                                                      VS




      pigure SFQX €lot of QR fe—ture s—mples @M0 A in Ph sp—™eD Vhc1 —nd Vhc2

ƒu˜tr—™tion of me—n v—lueD (gure SFRD from e—™h ve™torD Vhc1 —nd Vhc2 D equ—tion SFQFQF

                            M 0hc1 = Vhc1 − mean(Vhc1 )

                            M 0hc2 = Vhc2 − mean(Vhc2 )                         @SFQFQA




pigure SFRX €lot of QR norm—lised fe—ture s—mples @M0 A on two v—ri—˜les Vhc1 —nd
Vhc2


   Step2: covariance matrix
        VT                                             SFH    pe—ture input sp—™e redu™tion



„he ™ov—ri—n™e me—sure ‘P“ of two ve™tors X —nd Y D with me—ns of i{X } —nd i{Y }D

des™ri˜es the ˜eh—vior of their ™oEv—ri—˜ilityD —nd is given ˜y equ—tion SFQFRF

                      Cov(X, Y ) = E{[X − E{X}][Y − E{Y }]}.                        @SFQFRA

gov—ri—n™e ™—l™ul—tion is the multipli™—tion of di'eren™es ˜etween the ve™tors X =

x1 , x2 , . . . xn —nd Y = y1 , y2 , . . . , yn D —nd their me—n v—luesF „he v—lue of the

™ov—ri—n™e is interpreted —s followsX

e positive ™ov—ri—n™e indi™—tes th—t the two v—ri—˜les tend to move up —nd down

togetherD however — neg—tive ™ov—ri—n™e indi™—tes th—t when one moves higherD the

other tends to go lowerF

sn our ex—mple ™ov—ri—n™e m—trix is de(ned —sD equ—tion SFQFS

                                     cov(M 0hc1 , M 0hc1 ) cov(M 0hc1 , M 0hc2 )
    covmatrix (M 0hc1 , M 0hc2 ) =                                                  @SFQFSA
                                     cov(M 0hc2 , M 0hc1 ) cov(M 0hc2 , M 0hc2 )

…sing w—tl—˜ ™omm—nd ”cov” we get the following ™ov—ri—n™e m—trix v—luesD equ—E

tion SFQFTD of the d—t— presented in (gure SFR

                                                             0.7648 0.3700
               covmatrix (M 0hc1 , M 0hc2 ) = 1.0e−005 ∗                   .        @SFQFTA
                                                             0.3700 0.9944


   Step 3: calculation of eigenvectors and eigenvalues of covariance matrix
ƒin™e ™ov—ri—n™e m—trix is squ—reD it9s possi˜le to ™—l™ul—te the eigenve™tors —nd eigenE

v—lues for this m—trixF ƒome properties of eigenve™tors —re des™ri˜ed —s X

   • only the squ—re m—tri™es h—ve iigenve™torsD —nd not every squ—re m—trix h—s

      eigenve™torsF

   • —ll the eigenve™tors of — m—trix —re perpendi™ul—r @orthogon—lA iFeF —t right

      —ngles to e—™h otherD —nd it doesn9t depend on the dimension of this m—trixF
SFQF PCA illustr—tion                                                        VU



   • some m—tri™es do not h—ve —n eigenve™tor de™ompositionD „hese m—tri™es —re

      defe™tiveD or not di—gon—liz—˜leF e w—trix M is di—gon—lis—˜le if it is — squ—re

      m—trix —nd there is —n inverti˜le m—trix INV su™h th—t IN V −1 .M.IN V is —

      di—gon—l m—trixF


”pcacov” is — matlab ™omm—ndD whi™h ™omputes the eigenve™tors m—trix @Eigenvectorsmatrix AD

equ—tion SFQFU —nd the eigenv—lues m—trix @Eigenvaluesmatrix AD or €g v—ri—n™es @v—riE

—n™es of €rin™iple gomponentsAD equ—tion SFQFVF [Eigenvectorsmatrix , Eigenvaluesmatrix ] =

pcacov(covmatrix )

                                             −0.5931 − 0.8051
                     Eigenvectorsmatrix =                     .                   @SFQFUA
                                              −0.8051 0.5931

                                                       0.1267 0
                     Eigenvaluesmatrix = 1.0e−004 ∗             .                 @SFQFVA
                                                       0 0.0492

iigenve™tors m—trix of dimension 2 × 2D ™ont—ins P ™olumn ve™torsD e—™h of length PD

whi™h represent the P eigenve™tors of the ™ov—ri—n™e m—trix covmatrix F xote th—t ˜oth

of these eigenve™tors @Eigenvector1 —nd Eigenvector2 A h—ve ˜een s™—led to — unit
                             √
iFeF their module equ—l to IY 0.593122 + 0.805122 = 1F „he n—me ”Eigenvector” is

derived from the qerm—n word 4eigen4D —nd w—s (rst used in this ™ontext ˜y ril˜ert

in IWHRD it me—ns 4proper4 or 4own4F „he iigenv—lues m—trix @Eigenvaluesmatrix A

t—kes —lso the form of —n 2 × 2 di—gon—l m—trixD where the (rst v—lue (0.1267 ∗ 1e−4 ) is

˜igger th—n the se™ond one (0.0492 ∗ 1e−4 )F „h—t me—ns the (rst prin™iple ™omponent

@eigenvector1 A presents more d—t— v—ri—˜ility th—n the se™ond prin™iple ™omponent

@eigenvector2 AF

we—n v—lues —nd ™ov—ri—n™e m—trix —re ™—l™ul—ted from the d—t—D however iigenve™E

tors —nd eigenv—lues —re ™—l™ul—ted from the ™ov—ri—n™e m—trixF „he dire™tions of
         VV                                         SFH   pe—ture input sp—™e redu™tion




                   pigure SFSX €lot of (rst —nd se™ond iigenve™tors

eigenve™tors —re dr—wn in (gure SFS —s d—shed —nd doted linesF „he (rst eigenve™E

torD whi™h h—s the l—rgest eigenv—lue points to the dire™tion of l—rgest v—ri—n™e of

v—ri—˜lesD (gure SFSD in doted red lineD where—s the se™ond eigenve™torD whi™h is orE

thogon—l to the (rst one points to the dire™tion of less v—ri—˜les v—ri—n™eD (gure SFSD

in d—shed green lineF sn this ex—mple the (rst eigenv—lueD Eigenvalue1 = 0.1267D
                                                                                  −0.5931
in equ—tion SFQFV ™orresponding to the (rst eigenve™torD Eigenvector1 =           −0.8051
                                                                                            D

in equ—tion SFQFUF ‡hile the se™ond eigenv—lueD Eigenvalue2 = 0.0492D in equ—E
                                                                       −0.8051
tion SFQFV ™orresponding to the se™ond eigenve™torD Eigenvector2 =      0.5931
                                                                                 D in equ—E

tion SFQFUF fy ™omp—ring the v—lues of eigenv—lues we ™—n s—y th—t the (rst eigenve™tor

presents more v—ri—˜ilityF „he d—t— ™ould ˜e well —pproxim—ted with — Ih dimenE
                          −0.5931
sion—lD Eigenvector1 =    −0.8051
                                    D represent—tionF „he eigenv—lues —nd eigenve™tors

found —˜ove should s—tisfy the equ—tion SFQFW

  covmatrix ·   Eigenvectorsmatrix = Eigenvaluesmatrix      Eigenvectorsmatrix @SFQFWA
SFQF PCA illustr—tion                                                      VW



   VericationX
por the (rst prin™iple ™omponentD the v—lue of the left term of equ—tion SFQFW is given

in equ—tion SFQFIHD however the v—lue of the right term of equ—tion SFQFW is given in

equ—tion SFQFIIF


                                    covmatrix ·   Eigenvector1 =
                                0.7648 0.3700         −0.5931
                   1.0e−005 ∗                                 =
                                0.3700 0.9944         −0.8051
                                                        −0.0751
                                             1.0e−004 ∗                         @SFQFIHA
                                                        −0.1020


                         Eigenvalue1     · Eigenvector1 =
                                              −0.5931
                         1.0e−004 ∗ 0.1267            =
                                              −0.8051
                                                −0.0751
                                     1.0e−004 ∗                                 @SFQFIIA
                                                −0.1020
         WH                                        SFH   pe—ture input sp—™e redu™tion



   Step 4: Projection of original data onto Eigenvectors
„he origin—l d—t— setD M 0hc a [M 0hc1 , M 0hc2 ]D is proje™ted onto these two found

orthogon—l eigenve™tors @step QA @Eigenvector1 D —nd Eigenvector2 A (gure SFTF F „his




        pigure SFTX proje™ted d—t— s—mples onto (rst —nd se™ond eigenve™tors


proje™tion of d—t— s—mples onto these new —xis le—ds to ™re—tion of two prin™ip—l

™omponents P C1 —nd P C2 D (gure SFTF ‡e ™—n o˜serve th—t d—t— s—mples @v—ri—˜lesA

of (rst prin™ip—l ™omponent @P C1 A presented with ™ir™les —re good distinguish—˜leD

however the im—ges of v—ri—˜les of se™ond prin™ip—l ™omponent @P C2 A presented with

st—rsD —re less distinguish—˜leF


5.3.2 Graphical determination of eigenvectors
por sever—l dire™tions of these two orthogon—l eigenve™tors is possi˜le to get —fter d—t—

proje™tion di'erent prin™ip—l ™omponents —™™ording to their iigenve™tors9 dire™tionsF

„hese new redu™ed d—t— set h—ve di'erent v—ri—˜ilitiesD more the v—ri—˜ility is ˜ig less
SFQF PCA illustr—tion                                                        WI




pigure SFUX „he plot of ten @x, y A ™oordin—tes ™orresponding to ten unit eigenve™tors


we h—ve loss of inform—tion due to the tr—nsform—tion fun™tion ˜etween origin—l d—t—

sp—™e —nd new redu™ed d—t— sp—™eF „his v—ri—˜ility ™—n ˜e me—sured with v—ri—n™e

fun™tionF por ten di'erent dire™tions of unit proje™tion eigenve™torsD some v—lues

˜etween H —nd HFW of x —˜s™ise ™oordin—tes —re givenD ™ir™les in (gure SFUD —nd its ™orE

respondent y ™oordin—tes v—lues —re ™—l™ul—tedD squ—res in (gure SFUF gorrespondent

proje™ted d—t— v—ri—˜lesD for these ten unit proje™tion ve™torsD —re —lso ™—l™ul—ted —nd

presented in (gure SFVF fetween these ten produ™ed ™omponentsD through d—t— proje™E

tionD the ™omponent with higher v—ri—˜ility @or m—ximum v—ri—n™eA will ˜e ™onsidered

—s the prin™iple ™omponent @P C AF „he ™urve th—t ™onne™t —ll pre™edent ™—l™ul—ted

eigenv—lues is presented in (gure SFW F „hese iigenv—lues —re presented —s eigenve™tor

™oordin—tes @x, y AF „he interse™tion of the m—ximum v—ri—n™e v—lue of v—ri—n™e ™urve

with these ™oordin—tes in verti™—l lineD (gure SFIHD gives us the ™oordin—tes of the ˜est

iigenve™tor whi™h is ™onsidered —s prin™ip—l ™omponentF
        WP                                       SFH   pe—ture input sp—™e redu™tion




pigure SFVX ‚ot—tion of eigenve™tor inside Ph d—t— sp—™e in ten dire™tions —nd their
™orresponding €rin™ip—l gomponent ve™tors




pigure SFWX „he plot of ™urves of iigenv—lues ™orresponding to two orthogon—l iigenE
ve™tors
SFRF i0™ien™y of proje™tion method                                        WQ




       pigure SFIHX qr—phi™—l determin—tion of (rst iigenve™tor ™omponent


5.4 Eciency of projection method

ƒurf—™e iwq sign—lE˜—sed h—nd movement ™l—ssi(™—tion for the ™ontrol of prostheses

is ™onsideredF iwq surf—™e ele™trodes —re pl—™ed on two mus™le groupsX p—lm—ris

longus —nd extensor digitorumF prom the input fe—ture sp—™eD the ™l—ssi(erD see ™h—pE

ter TD should ˜e —˜le to ™l—ssify four h—nd movementsX )exion of the thum˜D the

pointer —nd the middle (nger movements —s well —s h—nd ™losingF „he initi—l p—rt

@400msA of e—™h single ™ontr—™tion period is extr—™ted from the r—w sign—l —nd —n—lE

ysed using ƒhort „ime pourier „r—nsform @ST F T AD see se™tion RFRFRF „his —n—lysis

method gives — me—sure of ˜oth time —nd frequen™y inform—tionF „hree relev—nt

fe—turesD moment of se™ond orderD ™entr—l frequen™y —nd st—nd—rd devi—tion see ™h—pE

ter R se™tion RFRFRD —re extr—™ted for e—™h ™h—nnelF „hree intelligent ™omput—tion—l

methodsD ‚—di—l f—sis pun™tion @RBF A networksD wultiEv—yer €er™eptrons @M LP A
           WR                                       SFH   pe—ture input sp—™e redu™tion



—nd ve—rning †e™tor u—ntiz—tion @LV QA networks —re used to distinguish ˜etween

our four di'erent types of h—nd movementsF sn (rst step the ™l—ssi(™—tion is —pplied

on e—™h fe—ture sep—r—tely using the —˜ove ™ited three methodsF sn the se™ond step

—ll three fe—tures —re ™onsidered together —s Th dimension—l fe—ture sp—™eF pin—llyD

the €rin™ip—l gomponents en—lysis @P CAA —lgorithm is —pplied to redu™e this Th

dimension—l fe—ture input sp—™e to Ph dimension—l input fe—ture sp—™eF

P CA is used to redu™e the dimension—lity of — d—t— set —nd to ret—in —s mu™h inforE

m—tion —s possi˜le of the relev—nt inform—tion in the origin—l multiEdimension—l input

fe—ture sp—™eF sn ™—se of fe—ture inst—n™es of ˜ig v—ri—˜ility in multiEdimension—l input

sp—™eD the —ppli™—tion of P CA —lgorithm m—y produ™e or le—d to — loss of inform—tion

whi™h give —s ™onsequen™e — de™re—se in ™l—ssi(™—tion —™™ur—™yF et the end of this

study —ll results will ˜e ™omp—red in t—˜les to resume the e'e™t of P CA dimension

redu™tion —lgorithm on surf—™e iwq sign—l ™l—ssi(™—tion in ™—se of relev—nt fe—ture

ve™torsF



5.4.1 Problem illustration
„he following (gure shows us three ™—ses of fe—ture set present—tionF „he ™l—ssi(™—E

tion t—sk ™—n use these three v—ri—nts of fe—ture present—tionF „he pro˜lem or the

question is to look for — ˜est v—ri—nt of fe—ture set present—tionD (gure SFIID to use for

™l—ssi(™—tionF „o —nswer this questionD e—™h type of these three fe—ture set present—E

tions for ™l—ssi(™—tion is studied —lone —nd in the end we ™omp—re them for the ™hoi™e

of the ˜est v—ri—nt —™™ording to their resultsF „he (rst fe—ture set present—tionD for

™l—ssi(™—tionD is ˜—sed on fe—ture sele™tion —mong n fe—turesD F 1, . . ., F nD —nd we

test e—™h fe—ture —loneF „his method —llows us to dis™rimin—te the ˜est fe—tures from
SFRF i0™ien™y of proje™tion method                                         WS




               f1
                                                             Reduced
               f2                                         p Dimensional
                           n Dimensional
                                               PCA          input space
                             input space
                           Presentation 2                      p<n
                                                          Presentation 3
               fn
          Presentation 1

              pigure SFIIX three ™—ses of d—t— set fe—tures present—tion

—notherF sn the se™ond fe—ture set present—tionD —ll our set fe—tures —re ™onsidered

together —nd —n n multi dimension—l sp—™e is ˜uildedD whi™h gives us ™lusters in m—ny

dimension—l —xisF „he third —nd l—st fe—ture set present—tion pro™edure ™onsiders —

redu™ed fe—ture sp—™e through line—r redu™tion P CA methodF „he question is whi™h

d—t— set present—tion should ˜e used for ™l—ssi(™—tionF „he —nswer should t—ke in

™onsider—tion not only the results ˜ut —lso the ™omplexity of gener—ted ™l—ssi(™—tion

modelsF



5.4.2 Features considered separately
1) Learning Vector Quantization classier model

LV Q networks ™—n ™l—ssify —ny set of input ve™torsD whi™h ™—n ˜e line—rly sep—r—˜le

or notF „he following t—˜le presents the v—lue r—nges of our four ™l—sses used ˜y LV Q

modelE™l—ssi(erF „he —r™hite™ture of this networkD (gure SFIPD resem˜les to th—t of

unsupervised ™ompetitive le—rning networkD ex™ept th—t e—™h output is —ssigned to

— t—rget ™l—ss —nd works in two stepsF pirst it uses —n unsupervised d—t— ™lustering

method to lo™—te sever—l ™lusters without using the inform—tion —˜out the num˜er
         WT                                               SFH       pe—ture input sp—™e redu™tion




                     „—˜le SFIX gl—ss r—nge for e—™h neuron output
              ™l—sses „—rget yutput yutput r—nge „ype of wovement
              gl—ssI        I              < IFS                     „hum˜ (nger
              gl—ssP        P             IFS E PFS                  €ointer (nger
              gl—ssQ        Q             PFS E QFS                  widdle (nger
              gl—ssR        R              > QFS                     r—nd ™losing

                                Input       Competitive   Output
                                layer       layer         layer




                                                          Class 1




                                                          Class 2




                 pigure SFIPX er™hite™ture ex—mple for LV Q network


of ™l—ssesF ƒe™ond it optimises the ™luster ™entres using a priori inform—tion —˜out

the num˜er of ™l—ssesF sn this type of networkD LV QD there is only one neuron

—'e™ted in the se™ond line—r l—yer for e—™h output ™l—ssF „he num˜er of ™lusters

™—n ˜e —lsoD a prioriD spe™i(edF „his network is —˜le to redu™e l—rge d—t— sets to —

sm—ller num˜er of ™ode˜ook ve™tors @™luster ™entresA suit—˜le for d—t— ™ompressingF

LVQ w—s introdu™ed ˜y „F uohonen ‘QT“F e new version with improved ™l—ssi(™—tion

perform—n™es h—ve ˜een proposed in ‘QV“F ƒin™e thenD it h—s ˜een widely used for —n

extensive ˜i˜liogr—phyF „he 4newlvq 4 fun™tion in w—tl—˜ progr—mm ™re—tes — two

l—yer networkF „his m—tl—˜ fun™tion use the le—rning fun™tion 4learnlv2 4 —™™ording

to the developed le—rning elgorithm v†P ‘QW“F sn the le—rning qu—ntiz—tion methodD

the weight in the hidden ™ompetitive l—yer —re re(ned —nd then the input ve™tor is

™l—ssi(ed to its t—rget ™l—ssF „his l—yer is p—rtitioned into groups of neuronsD e—™h one

is —sso™i—ted to — ™l—ssF
SFRF i0™ien™y of proje™tion method                                         WU



   a) Case of feature (M2) X

LV Q network used in this work h—s ˜een (rst tested for sever—l neuron num˜ers ™omE

posed the (rst ™ompetitive l—yer during PS tr—in epo™hsD see (gure SFIQD —nd then




pigure SFIQX gl—ssi(™—tion —™™ur—™y —nd glo˜—l num˜er of mis™l—ssi(ed inst—n™es for
di'erent num˜er of neurons in gompetitive l—yerF xum˜er of tr—ining epo™hs a PSF
pe—tureX wPF wethodXv†


the optim—l neurons num˜er foundD PU neurons in this ™—seD in ™ompetitive l—yer is

tr—ined —g—in during IHH tr—in epo™hsF sn (gure SFIR the —™™ur—™y ™l—ssi(™—tion —nd

mis™l—ssi(ed inst—n™es —re presented for e—™h type of movementF „he interferen™es

˜etween ™l—sses —re —lso presented to know ex—™tly the origin—l ™l—ss of e—™h mis™l—sE

si(ed inst—n™eF eddition—lly —re presented the glo˜—l ™orre™t ™l—ssi(ed inst—n™es —nd

the glo˜—l mis™l—ssi(ed inst—n™esF
        WV                                        SFH   pe—ture input sp—™e redu™tion




pigure SFIRX xum˜er of mis™l—ssi(ed inst—n™es for e—™h ™l—ss with PU neurons —nd
during IHH epo™hsF „his (gure shows even the numeri™—l distri˜ution of mis™l—ssi(ed
inst—n™es in other ™l—ssesF

   b) Case of feature (Fcent) X

„he s—me study is —pplied for the fe—ture F centF „he network LV Q h—s ˜een tested

for sever—l neuron num˜ers ™omposed the (rst ™ompetitive l—yerD —nd —n optim—l

model is found during PS tr—in epo™hsD see (gure SFISF „he ˜est one of themD IP

neurons in ™ompetitive l—yerD is tr—ined —g—in during IHH epo™hsF sn (gure SFIT

the —™™ur—™y ™l—ssi(™—tion —nd mis™l—ssi(ed inst—n™es —re presented for e—™h type of

movementF „he interferen™es ˜etween ™l—sses —re —lso presented to know ex—™tly the

origin—l ™l—ss of e—™h mis™l—ssi(ed inst—n™eF eddition—lly —re presented the glo˜—l

™orre™t ™l—ssi(ed inst—n™es —nd the glo˜—l mis™l—ssi(ed inst—n™esF
SFRF i0™ien™y of proje™tion method                                         WW




pigure SFISX gl—ssi(™—tion —™™ur—™y —nd glo˜—l num˜er of mis™l—ssi(ed inst—n™es for
di'erent num˜er of neurons in gompetitive l—yerF „he num˜er of tr—ining epo™hs a
PSF pe—tureX FcentF wethodX LVQ




pigure SFITX wis™l—ssi(ed inst—n™es with IP neurons —nd during IHH epo™hsF „his
(gure shows even the numeri™—l distri˜ution of mis™l—ssi(ed inst—n™es in other ™l—ssesF
        IHH                                      SFH   pe—ture input sp—™e redu™tion



   c) Case of feature (Fstd) X

„he s—me study is —pplied for the fe—ture F stdF „he network LV Q h—s ˜een tested for

sever—l neuron num˜ers ™omposed the (rst ™ompetitive l—yer during PS tr—in epo™hsD

see (gure SFIUF „he ˜est one of themD PP neurons in ™ompetitive l—yerD is tr—ined

—g—in during IHH epo™hsF sn (gure SFIV the —™™ur—™y ™l—ssi(™—tion —nd mis™l—ssi(ed




pigure SFIUX gl—ssi(™—tion —™™ur—™y —nd glo˜—l num˜er of mis™l—ssi(ed inst—n™es for
di'erent num˜er of neurons in gompetitive l—yerF „he num˜er of tr—ining epo™hs a
PSF pe—tureX pstdF wethodX v†


inst—n™es —re presented for e—™h type of movementF „he interferen™es ˜etween ™l—sses

—re —lso presented to know ex—™tly the origin—l ™l—ss of e—™h mis™l—ssi(ed inst—n™eF

eddition—lly —re presented the glo˜—l ™orre™t ™l—ssi(ed inst—n™es —nd the glo˜—l misE

™l—ssi(ed inst—n™esF

‡e resume —ll —˜ove results —˜out —™™ur—™y ™l—ssi(™—tion —nd mis™l—ssi(ed inst—n™es

of the fe—tures M 2D F cent —nd F std with LV Q ™l—ssi(™—tion method in the following

two (gures SFIW —nd SFPHF
SFRF i0™ien™y of proje™tion method                                        IHI




pigure SFIVX wis™l—ssi(ed inst—n™es with PP neuronsD —nd during IHH epo™hsF „his
(gure shows even the numeri™—l distri˜ution of mis™l—ssi(ed inst—n™es in other ™l—ssesF




pigure SFIWX qlo˜—l mis™l—ssi(ed inE           pigure SFPHX     gl—ssi(™—tion —™™uE
st—n™es for three fe—turesX M 2, F cent        r—™y ™orresponding to three fe—turesX
—nd F std using LV Q ™l—ssi(™—tion             M 2, F cent —nd F std using LV Q ™l—sE
methodF                                        si(™—tion methodF
        IHP                                        SFH   pe—ture input sp—™e redu™tion



2) Multi-Layer Perceptron networks

„his network is used in m—ny di'erent —ppli™—tionsF sts —r™hite™tureD (gure SFPID h—s

— l—rge ™l—ss of network types with m—ny di'erent topologies —nd tr—ining methodsF

wv€ h—s ˜een widely used for —n extensive num˜er of —ppli™—tionsF „he 4new 4

fun™tion in w—tl—˜ progr—mm gre—tes — feedEforw—rd ˜—™kprop—g—tion networkF peedE

forw—rd networks h—ve the following ™h—r—™teristi™sF €er™eptrons —re —rr—nged in

l—yersD inputs —re presented in the (rst l—yer —nd the l—st l—yer produ™ing outputsF

„he middle l—yers —re ™—lled hidden l—yers —nd don9t h—ve —ny ™onne™tions with the

extern—l worldF i—™h per™eptron in one l—yer is ™onne™ted to every per™eptron on the

next l—yerD —nd their inform—tion —re 4fed forw—rd4 from one l—yer to the nextF „he

size of the input —nd output l—yers —re de(ned —™™ording to the num˜er of system9s

inputs —nd outputsF rowever the num˜er of hidden neurons ™—n ˜e spe™i(ed —™™ording

to the needed perform—n™es —nd ™omplexity of the networkD for more det—ils see se™tion

TFPF „he num˜er of 4tansig 4 neurons in the hidden l—yer is determined ˜—sed on their

                              Input       Hidden      Output
                                          layer


                          x


                          y
                                                     Logsig


                                          Tansig


                pigure SFPIX er™hite™ture ex—mple for wv€ network


perform—n™e in tr—ining pro™essF „he oneEneuron outputEl—yer logEsigmoid tr—nsfer

fun™tion 4logsig 4is usedD whi™h gives —n output in the r—nge of H to IF yur output

r—nge ˜etween H —nd I will ˜e divided in four r—ngesD sin™e we h—ve four ™l—sses to ˜e
SFRF i0™ien™y of proje™tion method                                              IHQ




                   „—˜le SFPX gl—ss r—nge for e—™h neuron output
            ™l—sses „—rget yutput yutput r—nge „ype of wovement
            gl—ssI        HFIPS            HFHH   E   HFPS      „hum˜ (nger
            gl—ssP        HFQUS            HFPS   E   HFSH      €ointer (nger
            gl—ssQ        HFTPS            HFSH   E   HFUS      middle (nger
            gl—ssR        HFVUS            HFUS   E   IFHH      r—nd ™losing


identi(ed t—˜le SFPF


   „he MLP network used in this work h—s ˜een tested for sever—l neuron num˜ers

in the hidden l—yer during PS epo™hsF „he optim—l one found is tr—ined —g—in during

IHH epo™hsF „he —™™ur—™y ™l—ssi(™—tion —nd mis™l—ssi(ed inst—n™es —re ™—l™ul—ted for

e—™h type of movementF eddition—lly —re ™—l™ul—ted the —ver—ge —™™ur—™y —nd the

tot—l num˜er of mis™l—ssi(ed inst—n™esF „his s—me study is —pplied for e—™h fe—ture

for these following three fe—turesX M 2, F cent —nd F stdF ell results of ™l—ssi(™—tion

—™™ur—™y —nd mis™l—ssi(ed inst—n™esD ™orresponding to e—™h fe—tureD —re resumed —nd

presented in the following two (gures SFPP —nd SFPQF




pigure SFPPX qlo˜—l mis™l—ssi(ed inE                  pigure SFPQX     gl—ssi(™—tion —™™uE
st—n™es for three fe—tures X M 2, F cent              r—™y ™orresponding to three fe—turesX
—nd F std using M LP ™l—ssi(™—tion                    M 2, F cent —nd F std using M LP ™l—sE
methodF                                               si(™—tion method
        IHR                                         SFH      pe—ture input sp—™e redu™tion



3) Radial Basis Function networks

gomp—red to the MLP networkD the r—di—l ˜—sis fun™tion @RBF A network is the

next most used network modelD see se™tion TFSFQ for more det—ilsF „his xetworkD

(gure SFPRD is — one hidden l—yer neur—l xetwork with sever—l forms of r—di—l ˜—sis

—™tiv—tion fun™tionsD like ˜ell q—ussi—n fun™tionD whi™h is the ˜—sis fun™tion ™hosen for

the most ™ommonly used —ppli™—tionsF „he 4newrb 4 fun™tion in w—tl—˜ progr—mm

                               Input       Hidden     Output
                                           layer


                           x


                           y
                                                          Linear



                                           Gauss


                pigure SFPRX er™hite™ture ex—mple for RBF network


™re—tes — two l—yer networkF „he (rst l—yer ™ont—ins neurons of r—di—l ˜—sis fun™tions

—nd the se™ond ™ont—ins neurons of line—r fun™tionsF „his m—tl—˜ fun™tion ™re—tes —

new neuron for every iter—tionF „he error of the new network is ™he™kedD —nd if it

is not low enough the next neuron is —ddedF „his pro™edure is repe—ted until the

error go—l is metD or the m—ximum num˜er of neurons is re—™hedF „he output l—yer

is line—r —nd the r—te of ™l—ssi(™—tion is depending on the spre—d v—lue of the hidden

unitF ‡e give m—ny v—lues ˜etween HFI —nd I to (nd the optim—l spre—d v—lueF

„hese networks —re tr—ined during PS epo™hs for —ll three fe—turesF „he optim—l

spre—d v—lue found during PS tr—ining iter—tions is tr—ined —g—in during IHH epo™hsF

„he —™™ur—™y ™l—ssi(™—tion —nd mis™l—ssi(ed inst—n™es —re ™—l™ul—ted for e—™h type of

movementF eddition—lly —re ™—l™ul—ted the —ver—ge —™™ur—™y —nd the tot—l num˜er
SFRF i0™ien™y of proje™tion method                                              IHS




                „—˜le SFQX gl—ss r—nges for one line—r neuron output
            ™l—sses „—rget yutput yutput r—nge „ype of wovement
            gl—ssI        HFIPS            HFHH   E   HFPS      „hum˜ (nger
            gl—ssP        HFQUS            HFPS   E   HFSH      €ointer (nger
            gl—ssQ        HFTPS            HFSH   E   HFUS      middle (nger
            gl—ssR        HFVUS            HFUS   E   IFHH      r—nd ™losing




pigure SFPSX qlo˜—l mis™l—ssi(ed inE                  pigure SFPTX     gl—ssi(™—tion —™™uE
st—n™es for three fe—tures X M 2, F cent              r—™y ™orresponding to three fe—turesX
—nd F std using RBF ™l—ssi(™—tion                     M 2, F cent —nd F std using RBF ™l—sE
methodF                                               si(™—tion method

of mis™l—ssi(ed inst—n™esF „his s—me study is —pplied for e—™h fe—ture for our three

fe—turesX M 2, F cent —nd F stdF ell results ™on™erning —™™ur—™y ™l—ssi(™—tion —nd

mis™l—ssi(ed inst—n™esD ™orresponding to e—™h fe—ture —re resumed —nd presented in

(gures SFPS —nd SFPTF


4) Comparison of LVQ, MLP and RBF methods

‚esults ™omp—rison of —™™ur—™y ™l—ssi(™—tion —nd mis™l—ssi(ed inst—n™es of these three

fe—tures M 2, F cent —nd F std for —ll three ™l—ssi(™—tion methodsX LV Q, M LP —nd

RBF D —re ™omp—red —nd presented in the following (gures SFPU —nd SFPVF
        IHT                                        SFH   pe—ture input sp—™e redu™tion




pigure SFPUX    x˜ of tot—l misE                pigure SFPVX gl—ssi(™—tion —™™ur—™y
™l—ssi(ed inst—n™es for three fe—E              ™omp—rison ™orresponding to three
turesX M 2, F cent —nd F std using              fe—turesX M 2, F cent —nd F std using
LV Q, M LP —nd RBF ™l—ssi(™—tion                LV Q, M LP —nd RBF ™l—ssi(™—tion
methodsF                                        methods

5.4.3 Features considered together in 6D input space
sn the (rst p—rtD se™tion SFRFPD the ™l—ssi(™—tion w—s —pplied on e—™h fe—ture sep—r—tely

using the —˜ove ™ited three methods LV Q, M LP —nd RBF F sn this se™ond p—rt

of this ™h—pter our four movements will ˜e ™l—ssi(ed using —ll these three fe—tures

together in one Th input sp—™eD (gure SFPWF „he dis™ussion —˜out these results will

˜e done in se™tion SFSF



5.4.4 Feature space reduced in 2D space
€rin™iple gomponent en—lysis @P CAA —s — proje™tion method onto — low dimension—l

su˜sp—™e —ids to (lter out the uninteresting v—ri—˜lesF st t—kes in ™onsider—tion the

inter—™tions —nd ™orrel—tions ˜etween v—ri—˜lesF sn this third p—rt of studyD the input

sp—™e dimension of the origin—l d—t— fe—turesD whi™h is equ—l to sixD will ˜e redu™ed

to two dimension—l input sp—™eF „his pro™edure —llows us to present gr—phi™—lly

our fe—ture v—ri—˜lesF „he three networksD LV Q, M LP —nd RBF were tr—ined
SFSF ‚esults dis™ussion                                                  IHU




pigure SFPWX „opXgomp—rison of ™orre™t ™l—ssi(ed inst—n™es for e—™h movement ™orE
responding to six fe—tures togetherF fottomX gomp—rison of tot—l ™orre™tE —nd
misE™l—ssi(ed inst—n™es ™orresponding to six fe—tures togetherF sn ˜oth (gures
LV Q, M LP —nd RBF ™l—ssi(™—tion methods —re usedF

(rst during PS epo™hs for these two o˜t—ined fe—ture ve™tors using line—r dimension

redu™tion —lgorithm P CAF huring these PS tr—ining epo™hs we look for the optim—l

p—r—meters for e—™h methodX spre—d v—lueD num˜er of hidden neurons —nd num˜er

of neurons in ™ompetitive l—yer for respe™tively RBF, M LP —nd LV Q ™l—ssi(™—tion

methodsF ‡e tr—in —g—in our networks with these optim—l p—r—meters in Ph fe—ture

ve™tors sp—™e during IHH epo™hsF „he ™orre™t ™l—ssi(ed inst—n™es for e—™h type of

movement —nd the tot—l ™orre™t ™l—ssi(ed —nd mis™l—ssi(ed inst—n™es for —ll movements

—re ™—l™ul—tedF ell these results —re presented in (gure SFQHF



5.5 Results discussion
pirst the results of se™tion SFRFQ in ™omp—rison with se™tion SFRFR —re dis™ussedD see

(gures SFQI —nd SFQPF ƒe™ond it will ˜e ™onsidered the ™omp—rison of results ˜etween
        IHV                                         SFH   pe—ture input sp—™e redu™tion




pigure SFQHX „opX gomp—rison of ™orre™t ™l—ssi(ed inst—n™es for e—™h movement
™orresponding to Ph redu™ed fe—ture sp—™e with P CA for e—™h movement using
LV Q, M LP —nd RBF methodsF fottomX gomp—rison of tot—l ™orre™tE —nd misE
™l—ssi(ed inst—n™es num˜er ™orresponding to Ph redu™ed fe—ture sp—™e with P CAX
using LV Q, M LP —nd RBF ™l—ssi(™—tion methodsF

se™tion SFRFPD se™tion SFRFQD —nd se™tion SFRFRD see (gure SFQQF

   a) First discussion:

„he glo˜—l num˜er of mis™l—ssi(ed inst—n™esD for e—™h ™l—ssi(™—tion methodD in the

™—se of Th dimension—l fe—ture sp—™eD (gure SFQID is just little less th—n in the ™—se of

Ph dimension—l fe—ture sp—™eD (gure SFQPD o˜t—ined —fter —ppli™—tion of P CA redu™E

tion methodF ‡ith LV Q ™l—ssi(™—tion method there —re three mis™l—ssi(ed inst—n™es

more in ™—se of Ph redu™ed sp—™e th—n in Th sp—™eF ‡ith M LP ™l—ssi(™—tion method

there —re R mis™l—ssi(ed inst—n™es more in ™—se of Ph redu™ed sp—™e th—n in Th sp—™eF

ynly with RBF method we o˜serve —melior—tion ˜y one inst—n™e in ™—se of Ph reE

du™ed sp—™e th—n in Th sp—™eF „hese det—iled results —re resumed in t—˜le SFRF
SFSF ‚esults dis™ussion                                              IHW




pigure SFQIX g—se of se™tion SFRFQY        pigure SFQPX g—se of se™tion SFRFRY
„opX gomp—rison of ™orre™t ™l—ssi(ed       „opXgomp—rison of ™orre™t ™l—ssi(ed
inst—n™es num˜er for e—™h movement         inst—n™es num˜er for e—™h movement
™orresponding to Th fe—ture sp—™eF         ™orresponding to Ph redu™ed fe—ture
fottomXqlo˜—l num˜er of mis™l—ssiE         sp—™e with P CAF fottomX„ot—l numE
(ed inst—n™es ™orresponding to Th fe—E     ˜er of mis™l—ssi(ed inst—n™es ™orreE
ture sp—™eF …sing LV Q, M LP —nd           sponding to Ph redu™ed fe—ture sp—™e
RBF ™l—ssi(™—tion methods for ˜oth         of Th fe—ture sp—™e with P CAF …sing
™—sesF                                     LV Q, M LP —nd RBF methods




„—˜le SFRX glo˜—l num˜er of mis™l—ssi(ed inst—n™es ™omp—rison ˜etween Th fe—tures
sp—™e —nd redu™ed Ph fe—tures sp—™e for LV Q, M LP —nd RBF ™l—ssi(™—tion methods
                      wethods Th sp—™e Ph redu™ed sp—™e
                          LVQ        T            W
                          MLP        T            IH
                          RBF       IQ            IP
        IIH                                       SFH   pe—ture input sp—™e redu™tion




pigure SFQQX g—se of se™tion SFRFPY qlo˜—l num˜er of mis™l—ssi(ed inst—n™es for e—™h
fe—tureX M 2, F cent —nd F std using LV Q, M LP —nd RBF ™l—ssi(™—tion methodsF


   b) Second discussion:

xow the ™l—ssi(™—tion results using LV Q, M LP —nd RBF methods for e—™h fe—ture

sep—r—telyD whi™h is done in se™tion SFRFPD is ™onsideredF „hese resultsD (gure SFQQ

show us how relev—nt —re these fe—turesF „he third fe—tureD FstdD —lone in Ph diE

mension—l sp—™e @F std channel1 —nd F std channel2 A gives less —ver—ge num˜er of

mis™l—ssi(ed inst—n™es with these three methodsD whi™h equ—l to UDQQ th—n in the ™—se

of Ph dimension—l redu™ed fe—tures sp—™eD whi™h gives —n —ver—ge num˜er of mis™l—sE

si(ed inst—n™es equ—l to IHDQQF sn t—˜le SFS —ll results found in se™tions SFRFPD SFRFQ

—nd SFRFR —re resumed —nd ™omp—redF




5.6 Conclusion
qener—lly the €rin™ip—l gomponent en—lysis method le—ds to — more dis™rimin—ted

represent—tion of d—t—F „he sp—ti—l redu™tionD in this studyD for ™l—ssi(™—tion issue
SFTF gon™lusion                                                           III




„—˜le SFSX glo˜—l num˜er of mis™l—ssi(ed inst—n™es ™omp—rison ˜etween Th fe—tures
sp—™e —nd redu™ed Ph fe—tures sp—™e for LV Q, M LP —nd RBF ™l—ssi(™—tion methods
  wethods      Th sp—™e Ph redu™ed sp—™e       Ph sep—r—ted three fe—tures sp—™e
    LV Q           T                W             M2 aIU Fcent aPHD       Fstd aU
   M LP            T               IH             M2 aIT Fcent aQID       Fstd aT
   RBF            IQ               IP             M2 aIR Fcent aIRD       Fstd aW
 ever—ge x˜       VDQQ           IHDQQ         M 2XISDTT F centaPIDTT     F stdaUDQQ


using P CAD h—s not le—d to — ˜etter resultsF ren™e for relev—nt fe—turesD this proE

™edure of sp—™e redu™tion m—y de™re—se this dis™rimin—tion ˜etween d—t— groupsF sn

this study the fe—ture F std in Phimension—l fe—ture sp—™e gives ˜y it self —n —ver—ge

num˜er of mis™l—ssi(ed inst—n™esD whi™h is equ—l to UDQQD less th—n in the ™—se of PhiE

mension—l redu™ed sp—™eD whi™h gives —n —ver—ge num˜er of mis™l—ssi(ed inst—n™es

equ—l to IHDQQF „herefor in this thesis —nd for —ll following studies the fe—tures —re

™onsidered sep—r—telyF
IIP   SFH   pe—ture input sp—™e redu™tion
Chapter 6
Performances of proposed FTMC
algorithm

6.1 Introduction
„he go—l of re™ognition @™l—ssi(™—tionA pro™edure is to ˜uild — set of models th—t

™—n ™orre™tly predi™t the right ™l—sses for di'erent o˜je™ts @fe—turesAF „his pro™edure

is performed on the ˜—sis of extr—™ted fe—tures through ˜uilded ™l—ssi(™—tion modE

elsF gl—ssi(™—tion models ˜elong to two ™—tegoriesF pirst —re supervised modelsD like

wultiEv—yer €er™eptronD ‚—di—l f—sis xetworksD —nd ve—rning †e™tor u—ntiz—tion

networkF ƒe™ond —re unsupervised modelsD like ƒelf yrg—nizing w—pD puzzy ƒu˜E

tr—™tive glustering —nd gompetitive v—yerF „here is — l—rge set of neur—l networks

—nd fuzzy logi™ methods in the liter—ture —ddressing ™l—ssi(™—tion pro˜lemsF „hese

methods in ™—se of supervised le—rning employ optimis—tion te™hniques to pro™ess

the inputs —nd ™omp—re their resulting outputs —g—inst the desired outputsF irrors

—re then ™—l™ul—tedD ™—using the system to —djust its p—r—metersF sn ™—se of unsuE

pervised le—rningD tr—ining —lgorithms —ttempt to lo™—te ™lusters in the input d—t—D

whi™h —pproxim—te the distri˜ution of the d—t—D without a prior knowledgeF wore

                                         IIQ
        IIR                         TFH   €erform—n™es of proposed p„wg —lgorithm



det—ils —˜out ™lustering d—t— in ‘RP“F Hykin pu˜lished — ™omprehensive found—tion

for the study of xeur—l xetworks ‘PU“D J. -S. R. JangD C. -T. Sun —nd E. MizutaniD

pu˜lished — ˜ook —˜out — found—tion of xeuroEpuzzy systemsD ‘QI“F ell these methods

h—ve fun™tions p—r—meters —nd v—ri—˜les to ˜e optimisedF

„he o˜je™tive in this ™h—pter is (rst to des™ri˜e ˜rie)y the known ™l—ssi(™—tion proE

™eduresD ˜—sed on puzzy logi™ —nd xeur—l xetwork methodsD moreover — proposed

puzzy „rimmed we—n gl—ssi(™—tion @F T M C A —lgorithm will ˜e des™ri˜edF ƒe™ond

o˜je™tive is to ™omp—re ˜etween these di'erent intelligent ™omput—tion—l methodsX

wultiEv—yer €er™eptron @M LP AD ‚—di—l f—sis pun™tion xetworks @RBF AD ve—rning

†e™tor u—ntiz—tion network @LV QAD proposed puzzy „rimmed we—n gl—ssi(™—tion

@F T M C A —lgorithmD —nd fuzzy ƒu˜tr—™tive glustering @F SC AF



6.2 Neural Network Systems
„his se™tion des™ri˜es ˜rie)y the —r™hite™tures —nd le—rning pro™edures of —d—ptive

neur—l networks @AN N AF †—rious AN N E˜—sed models ‘W“ were —pplied to identify

di'erent systemsF „here —re m—ny fun™tions —nd v—ri—˜lesD whi™h should ˜e identi(ed

for e—™h neur—l network modelF xeur—l networks pro™ess inform—tion in — simil—r

w—y the hum—n ˜r—in doesF st is — network stru™ture ™onsisting of — l—rge num˜er of

inter™onne™ted pro™essing neuronesD through dire™tion—l linksD working in p—r—llel to

solve — spe™i(™ pro˜lemF i—™h neurone h—s —n —d—ptive inter—™tion with —notherF „he

le—rning methods spe™ify how these inter—™tions should ˜e upd—ted to minimise error

me—sure ˜etween the desired —nd ™omputed output d—t— setsF „here —re m—ny le—rning

methods to ˜uild neur—l modelsF qener—lly —n —d—ptive network is heterogeneous —nd

e—™h neuron h—s — spe™i(™ fun™tion di'erent from the othersF st is possi˜le to ™l—ssify
TFPF xeur—l xetwork ƒystems                                             IIS



these model le—rning methods —nd —r™hite™turesF



6.2.1 Architecture
e simple —r™hite™ture of —n —d—ptive neur—l network is expressed in this following

m—them—ti™—l fun™tion with p—r—meter p —nd v—ri—˜les @xD y AD —nd presented in (gE

ure TFIF

   w—them—ti™—l fun™tionX y = f (x, p)

                              x            f             y


                                  p

                  pigure TFIX ƒimple per™eptron with one output unitF


   F

en —d—ptive network with only one neuron is shown in (gure TFID whi™h h—s the

fun™tion f D where x —nd y —re the input —nd output setsD —nd p is — p—r—meter to ˜e

optimisedF



6.2.2 Example of illustration
‡e w—nt to ˜uild —n —d—ptive networkD whi™h ™—n give the result of — simple su˜tr—™E

tive fun™tion f ˜etween two re—l num˜ers x1 and x2 F

„his fun™tion is given —sX y = f (x, p)F de(ned in   2
                                                         →

„he v—ri—˜les —reX

x = [x1 , x2 ]D p = [w1 , w2 ] —nd y

„he su˜tr—™tive fun™tion is de(ned —sX
        IIT                          TFH   €erform—n™es of proposed p„wg —lgorithm



y = w1 × x1 + w2 × x2

yur t—sk is to (nd the v—lues of w1 —nd w2 D whi™h ™—n produ™e — ™orre™t su˜tr—™tion

output result for —ll inputsF

por this ex—mple we test —ll the v—lues of w1 —nd w2 ˜etween EP —nd PF „he errors

™orresponding to e—™h ™ouple of @ w1 —nd w2 A —re ™—l™ul—ted for some ex—mple v—lues

of x1 D —nd x2 F st is o˜vious th—t the v—luesX w1 a ID —nd w2 a EI —re the right v—lues

to —™hieve the fun™tion of su˜tr—™tion in the following oper—tion X y = x1 − x2 D ˜ut

we will show how pro™eeds —n —d—ptive neur—l network to (nd this solutionF



1) Learning procedure to nd optimised w1 and w2

„he question now is how does work the xeur—l xetworks to (ndD with le—rning proE

™edureD these two p—r—meter v—lues of w1 —nd w2 F „he —d—ptive pro™edure to (nd w1


„—˜le TFIX ƒome ex—mple v—lues of input —nd their output results for the fun™tion of
su˜tr—™tion f
                      snput I snput P         yutput
                         x1        x2     y = w1 x1 + w2 x2
                             I         P              EI
                            IP         S               U
                            ER         T             EIH
                            EP        ES               Q



—nd w2 should use only some v—lues of inputEoutput sets —s tr—ining d—t— —nd then

we hope th—t these found w1 —nd w2 v—lues will give the ™orre™t results of su˜tr—™tion

for —ll other input v—lues of x1 and x2 F sn the t—˜le TFI some tr—in v—lues of x1 and x2

—re given with their ™orresponding outputs y F

sn this ™l—ssi™—l ex—mple it will ˜e shown the simplest intelligent selfEle—rning model
TFPF xeur—l xetwork ƒystems                                                     IIU



@single per™eptronA th—t ™—n —d—pt its p—r—meters to —™hieve @or giveAthe desired outE

putF „he —r™hite™ture of this neur—l networkD is shown in (gure TFPD F

                             W1
                  x1
                                                           Output y

                             W2
                                                    Σ
              x2

                                               t-y                    Targe t




                  pigure TFPX er™hite™ture of ƒimple neur—l network NNF


„he output y of — network is — weighted line—r ™om˜in—tion of inputs x1 and x2 D

equ—tion TFPFIF

                                      y=           wi xi                              @TFPFIA
                                           i=1,2

„he me—sure error is given in equ—tion TFPFPF

                                      E = (t − y)2                                    @TFPFPA

where t design — t—rget outputF


2) Derivative-based optimisation method

„he o˜je™tive fun™tion E is de(ned on — Ph dimension—l input sp—™e wF „his input

sp—™e is given in equ—tion TFPFQF

                                     w = [w1 , w2 ]T                                  @TFPFQA

„he —im is to (nd the ve™tor w = w∗ whi™h minimizes our o˜je™tive fun™tion E(w)F

„he gr—dient of di'erenti—˜le fun™tion E is — ve™tor of (rst deriv—tives of E D denoted
          IIV                         TFH      €erform—n™es of proposed p„wg —lgorithm



—s g in equ—tion TFPFRF

                          g(w) = [∂E(w)/∂w1 , ∂E(w)/∂w2 ]T                         @TFPFRA

„he per™eptron in (gure TFP is tre—ted —s — single l—yer per™eptronF ƒt—rting with — set

of initi—l weights @w0 AF ve—rning —lgorithm for this singleEl—yer per™eptron is —™hieved

in these two following steps until the ™onvergen™e of weights to the —™™ept—˜le v—lues

is re—™hedF „hese optimised weights —llow the network to give — right t—rget outputF

  IF sele™t —n input ve™tor x = [x1 , x2 ]

  PF —d—pt the weights w1 —nd w2 if the output y is f—lseF

„he well known steepest formul— th—t used to —d—pt the weights w1 —nd w2 is de(ned

in equ—tion TFPFSF

                                w(t + 1) = w(t) − ηg(w)                            @TFPFSA

where η is the le—rning r—teF

„he given tr—ining d—t— set h—s R p—irsD —nd the over—ll error me—sure is de(ned —s

the following squ—red sum in equ—tion TFPFTF

                             E=            (Ep )2 , Ep = tp − yp                   @TFPFTA
                                   p=1,4

where pX index num˜er of tr—ining d—t— p—irsD tp X desired outputD —nd yp X predi™ted

outputF

„he deriv—tive of the error with respe™t to e—™h weight —re given in equ—tions TFPFUD TFPFVD

—nd TFPFWF

                           ∂E(w)/∂wi = −2                    (tp − yp )xip         @TFPFUA
                                                     p=1,4

                     ∂E(w)/∂w1 = −2                (tp − w1 x1p − w2 x2p )x1p .    @TFPFVA
                                           p=1,4
TFPF xeur—l xetwork ƒystems                                                            IIW



                        ∂E(w)/∂w2 = −2                 (tp − w1 x1p − w2 x2p )x2p .          @TFPFWA
                                               p=1,4

sf the initi—l v—lues of w1 —nd w2 —re EIFV —nd IFVD the steepest des™ent minimis—tion

—lgorithm givesD —fter QH iter—tions with η a HFHID the following le—rning ™urve ™onE

vergen™eD (gures TFQ —nd TFRF „his ex—mple illustr—tes how the —lgorithm follows the

gr—dient downD on the errorEsurf—™eD to re—™h the optimised v—luesD whi™h —re equ—l

to (w1 = 1, and w2 = −1)F

     „his ex—mple represents the simplest neur—l network @N N A modelF st provides

                                                                   2


                                                              w2   1


                                                                   0

                                           2
                                                                   -1
 0                                 0
-2       -1    0        1                                          -2
                            2 -2     w2                             -2    -1       0   1      2
                   w1                                                             w1


pigure TFQX ƒteepest des™ent ™onverE                        pigure TFRX ƒteepest des™ent ™onverE
gen™e @QhAF                                                 gen™e @PhAF


the ground for other ™omplex N N models like wultiEv—yerE€er™eptron @M LP AF „he

neurons of ˜—™kprop—g—tion wultil—yer €er™eptrons @M LP A —re — ™omposite of the

weighted sum —nd — di'erenti—˜le nonline—r —™tiv—tion fun™tion @tr—nsfer fun™tionAF„he

most used —™tiv—tion fun™tions in ˜—™kEprop—g—tion M LP —reX


      • vogisti™ fun™tionX f (x) =       1
                                       1+e−x
                                             F

                                                         1−e−x
      • ryper˜oli™ t—ngent fun™tionX f (x) =             1+e−x
                                                               F


      • sdentity fun™tionX f (x) = xF
        IPH                            TFH   €erform—n™es of proposed p„wg —lgorithm



„he gr—dient ve™tor in this type of NN models is ™—l™ul—ted in the opposite dire™tion

to the )ow of the output of e—™h neuronF yn™e the gr—dient is o˜t—ined D it is possi˜le

to —pply m—ny methods of deriv—tiveE˜—sed optimis—tionD whi™h will ˜e des™ri˜ed in

the following se™tion TFPFQF


6.2.3 Gradient-based optimisation methods
„his se™tion gives —n introdu™tion to nonline—r optimis—tion te™hniques using deriv—tiveE

˜—sed method su™h —s gr—dientE˜—sed optimis—tion —lgorithmF yptimis—tion is the

pro™ess to (nd the v—lues of — ve™tor Θ th—t minimises — given fun™tion f de(ned on

—n n-dimensional input sp—™e ΘF w—ny —lgorithms for minimising f (Θ) —re derived

from —lgorithmsD whi™h —re used for solving the following equ—tion TFPFIHF

                                  g(Θ) = ∂f /∂Θ = 0.                            @TFPFIHA

g is the gr—dient of — di'erenti—˜le fun™tion f X   n
                                                        →

st is often useful to use —lgorithmsD whi™h pro™eed iter—tively st—rting from —n —pproxE

im—te tri—l solution —nd then will gr—du—lly re(ne the v—lues of p—r—meters of ve™tor

Θ until the predetermined pre™ision is re—™hedF „he next point Θnext D in iter—tive deE

s™ent pro™edureD is determined ˜y — le—rning r—te @stepEdownA from the ™urrent v—lue

Θnow in the dire™tion ve™tor dv D equ—tion TFPFII

                                 Θnext = Θnow + ρdv.                            @TFPFIIA

where ρ X represent — le—rning r—teF

dv @des™ent ve™torAX is — ve™tor of des™ent dire™tion th—t moves us ™loser tow—rds —

lo™—l minimum Θ∗ of our o˜je™tive fun™tion f X       n
                                                         →   F

hes™ent methods ™—l™ul—te the term dv in two stepsX (rst step is determin—tion of
TFPF xeur—l xetwork ƒystems                                               IPI



the dire™tion ve™tor dv D —nd in the se™ond step is ™—l™ul—tion of le—rning r—te ρF „he

v—lues of next ve™tor Θnext should s—tisfy the inequ—lity in equ—tion TFPFIPF


                              f (Θnow ) > f (Θnow ) + ρdv.                      @TFPFIPA


ρ must ˜e ™hosen so th—t we don9t t—ke too ˜ig or too sm—ll v—lue of stepD —nd the

v—lue of the step size is —llowed to ˜e ™h—nged —t every iter—tionF

ell des™ent —lgorithms look for to re—™h the minimum point following the line deterE

mined ˜y the ™urrent v—lue of Θnow —nd the dire™tion dv F ivery des™ent —lgorithm

h—s its own method to ™hoose the w—y of su™™essive dire™tionsF


1) Mathematical description

„he —im of these methods for — given o˜je™tive fun™tion f is to redu™e the v—lue of

this fun™tion —fter every iter—tionF „he (rst deriv—tives of — di'erenti—˜le fun™tion

f —t the v—lues of ve™tor p—r—meters Θ represent the gr—dient ve™tor g de(ned in

equ—tion TFPFIQF

                             g(Θ) = ∂f (Θ)/∂(Θ) =       f.                      @TFPFIQA

qr—dient ˜—sed optimis—tion str—tegies se—r™h iter—tively the minimum of the o˜je™tive

fun™tion f D —nd it pro™eeds in the three following stepsX

   • ™ompute the o˜je™tive fun™tion f (Θnow ) using the initi—lis—tion ve™tor v—lues

     Θinitial

   • ™ompute the ve™tor dire™tion dv —nd — step width ρF

   • ™ompute of the new point Θnext = Θinitial + ρdv Y —nd go to step I until to re—™h

     the optimum Θ∗
          IPP                            TFH   €erform—n™es of proposed p„wg —lgorithm



„he line—r —pproxim—tion @(rst orderA of the o˜je™tive fun™tionD f D is given in equ—tion

TFPFIRF

                           f (Θnow + ρ dv) ≈ f (Θnow ) + ρ g T dv.                  @TFPFIRA

„he ™ondition of error ™onvergen™e is th—t 4g T dv 4 must ˜e neg—tiveD hen™e we will

h—ve f (Θnow + ρdv) < f (Θnow )D this ™ondition is des™ri˜ed in equ—tion TFPFIPF

†—rious methods —re —v—il—˜le to ™ompute des™ent dire™tionsD likeX gr—dient des™entD

™onjug—te gr—dient methodD xewton9s method —nd Levenberg EM arquardt methodF

yne ™ondition must ˜e hold in use of these methodsX the —ngle ˜etween the gr—dient

ve™tor g —nd des™ent ve™tor dire™tion dv D equ—tion TFPFISD must ˜e in the —re— of 90◦

—nd 270◦ D see (gure TFSF „he gr—dient dire™tions —re —lw—ys perpendi™ul—r to the

™ontour ™urvesF


     Θnext = Θnow + ρ dv g = Θnow + ρ           g     dv       cos (angle(g, dv))   @TFPFISA


„he dire™tions from the st—rting point Θnow D (gure TFSD whi™h shows the surf—™e error

                          2
                                                        g(Өnow)
                          1
                     w2




                          0
                                                           dv

                          -1


                          -2
                           -2       -1           0         1          2
                                                w1

          pigure TFSX possi˜le des™ent dire™tions from the st—rting point Θnow F
TFQF xeuroEfuzzy systems                                                      IPQ



of our ex—mple in se™tion TFPFPFID —re the —ll —™™ept—˜le des™ent ve™tors possi˜ilitiesF sf

dv = −g D @—ngle@g, dv) = 180◦ AD this des™ent is ™—lled the steepest des™ent methodD in

whi™h dv represents the s—me dire™tion —s the neg—tive gr—dient dire™tion @−g AF „he

neg—tive gr—dient dire™tion is notD —lw—ysD — short w—y to re—™h the minimum Θ∗ F por

this re—son m—ny other methods likeX ™onjug—te gr—dient methodD xewton9s method

—nd Levenberg EM arquardtD —re developed to dire™tD qui™kly —s possi˜leD tow—rd the

minimum point of o˜je™tive fun™tion f F por more det—ils see ‘QI“F

qener—lly the deriv—tiveE˜—sed optimis—tion methods —re used to (nd the ne—rest

lo™—l minimum of —n o˜je™tive fun™tionD whi™h presupposes th—t the gr—dient of this

fun™tion is ™omput—˜leF st st—rts from the point Θnow —nd moves in the dire™tion of

the following ve™tor de(ned in equ—tionD TFPFITX

                                  g    cos (angle(g, dv))                           @TFPFITA




6.3 Neuro-fuzzy systems
„he fuzzy inferen™e is — —n intelligent ™omputing method ˜—sed on the ™on™epts of

fuzzy set theoryD Lotf i A. Zadeh ‘TW“F „his method h—s m—ny —ppli™—tions in v—riety

of dom—ins likeX ™ontrolD time series predi™tionD ro˜oti™sD systems modellingD —nd

p—ttern re™ognitionsF „he fuzzy rules represent — hum—n knowledgeD expressed in

n—tur—l l—ngu—geD using fuzzy words @in —n —pproxim—te m—nnerAF ‡ith help of the

™omposition rules of inferen™e it will ˜e possi˜le to formul—te this knowledge of fuzzy

re—soning in m—them—ti™—l rel—tionsF „his new —ppro—™h of the —n—lysis of n—tur—l

physi™—l systems —llows us toX

   • introdu™e the knowledge into — model systemF
         IPR                           TFH   €erform—n™es of proposed p„wg —lgorithm



   • re(ne this knowledge ˜y t—king in ™onsider—tion model errorsF

„he puzzy snferen™e ƒystems @F IS A —re ™omposed of — ™olle™tion of rules whi™h h—ve

the gener—l formX

                     If such Situation then such Conclusion.

e situ—tion is ™h—r—™terized ˜y ™ert—in num˜er of expressions of the type x is AD where

x is — v—ri—˜le —nd A — l—˜elF st is ne™ess—ryD for the oper—tion—l ph—seD to interpret

the qu—lit—tive set to the qu—ntit—tive setD or the su˜je™tive set with the o˜je™tive

setF „h—t is ™—rried out prim—rily ˜y the ™hoi™e of the expression universe —nd the

mem˜ership fun™tions whi™h will de(ne pre™isely to whi™h degree x is AF „here —re

two v—rious types of FISD whi™h —re m—inly usedX

E M amdaniD —nd

E T akagiESugeno —nd Kang F

sn our thesisD the se™ond type of F IS D T akagiESugeno —nd Kang model ‘TU“D is

usedF „he m—in di'eren™e ˜etween M amdani —nd Sugeno is th—t the Sugeno output

mem˜ership fun™tions —re either line—r or ™onst—ntF „his type is ˜—sed on rules where

the —nte™edent is ™omposed of linguisti™ v—ri—˜les —nd the ™onsequen™e is represented

˜y — line—r fun™tion of input v—ri—˜lesF „he most used form for this type of F IS

models is shown in the following equ—tionD TFQFID in whi™h the ™onsequen™e ™onstitutes

— line—r ™om˜in—tion of v—ri—˜les implied in the —nte™edentF

   if x1 is A1 and . . . . xn is An T hen Y = p1 x1 + . . . + pn xn + p0        @TFQFIA

whereX

xi X —re input v—ri—˜les of the system

Y X is output v—ri—˜le of the system
TFQF xeuroEfuzzy systems                                                IPS



pi X re—l v—ri—˜les

Ai X —re p—r—meters of su˜sets @mem˜ershipEfun™tionsAD whi™h de(ne the degree of

mem˜ershipD ˜etween H —nd ID of e—™h point of the input sp—™eD ™orresponding to

linguisti™ l—˜elsF

„he output of — T akagiESugeno —nd Kang model using puzzy snferen™e ƒystem

™omposed of m rules is formul—ted —s — weighted —ver—ge of the individu—l outputsD

yi : i = 1 . . . , mD provided ˜y e—™h ruleD equ—tion TFQFPF

                                      i=1,...,m wi yi
                                                                              @TFQFPA
                                       i=1,...,m wi

where wi X is the produ™t of mem˜ership degrees of inputs xi for ™orresponding memE

˜ership fun™tionsF

e Sugeno system is suited for modeling nonline—r physi™—l phenomenon @pro™ess

systemsA ˜y interpol—ting ˜etween multiple line—r modelsD ˜e™—use of the line—r deE

penden™e of e—™h rule on the input v—ri—˜les of — systemF

puzzy systems —re knowledgeE˜—sed models ™onstru™ted from — ™olle™tion of linguisti™

spE„rix rulesD whi™h need —utom—ti™ tuning of their p—r—meters like the ™enter —nd

˜—sis of mem˜ership fun™tions F w—ny rese—r™hers in the fuzzy ™ommunity h—ve ™onE

sidered xeur—l xetworks @N N A to provide for fuzzy models the ™—p—™ity of —utom—ti™

p—r—meters selfEtuneF „hey —im to ™onjug—te —nd ™om˜ine ˜etween le—rning —˜ility

of N N —nd re—soning —˜ility of F IS F sn xeur—l xetworks the inform—tion —˜out

the system ™onsist in the v—lues of inputs —nd outputs without (xed model stru™tureD

whi™h is ™onsidered ™onsequently —s ˜l—™kE˜ox model ‘SH“F sn this ™—se the p—r—meters

h—ve no signi(™—nt physi™—l sense @no interpret—˜ilityAD —nd no physi™—l des™ription

of their ™orresponding re—l systemsF roweverD in fuzzy modelsD —v—il—˜le prior knowlE

edge —˜out the system —llows the ™onstru™tion of knowledgeE˜—sed modelsF ‡ith
          IPT                       TFH   €erform—n™es of proposed p„wg —lgorithm



fuzzy logi™ method it is possi˜le to introdu™e or integr—te su™h prior knowledge of

the system into the m—them—ti™—l modelF efter this introdu™tion —˜out these two —pE

pro—™hesD it is ne™ess—ry to notify th—t the hy˜ridising ˜etween them @N euro−F uzzy

ƒystemsA to improve the ˜eh—viour of their resulting models for either modelling or

™l—ssi(™—tion of systemsD le—d gener—lly to the loss of the physi™—l interpret—tion of

the v—rious F IS 9 p—r—metersF „his noti(™—tion is given ˜e™—use the notion of the

snterpret—˜ility of F IS must ˜e ™onsidered in su™h hy˜rid N euro − F uzzy ƒystemsF

ytherwiseD the resulting optimised modelsD whi™h —re knowledgeE˜—sed models ˜efore

optimis—tionD loss the notion of knowledge —nd will ˜e uninterpretedF „o preserve

the notion of modelEinterpret—tion in ™—se of neuro-fuzzy systemsD it is ne™ess—ry to

require some ™onstr—ints on their optimis—tion methodsF

sn the next se™tionD TFRD hy˜rid supervised —ppro—™hD puzzy „rimmed we—n gl—ssi(™—E

tion @F T M C A —lgorithm is proposedF „his —ppro—™h is m—them—ti™—l deriv—tiveE˜—sed

optimis—tion methodD without introdu™ing of xeur—l xetworksF „rimmed me—nE˜—sed

rules initi—lis—tion gives —n interpreted optimised (n—l ™l—ssi(erEmodel in this —pE

pro—™hF



6.3.1 Neuro-fuzzy systems architecture
sn the pre™eding two se™tionsD TFP —nd TFQD ˜oth fuzzy logi™ systems —nd neur—l network

systems —re des™ri˜edF „he hy˜rid system known —s neuro-fuzzy system h—s ˜een

˜e™—me worldwide tool for m—ny rese—r™hers in this (eld —nd found its ˜irth in the

in™re—se of ™omplexity of systems —nd their identi(™—tionF hi'erent —r™hite™tures of

neuro-fuzzy system h—ve ˜een investig—ted ˜y num˜er of rese—r™hersF

sn ™—se of (rst order T akagiESugeno —nd Kang systemD the fuzzy inferen™e systemD
TFQF xeuroEfuzzy systems                                                IPU



for two inputs x —nd y —nd one output z D ™—n ˜e presented —s ex—mple of four rulesF

i—™h input sp—™e is presented with two mem˜ership fun™tions in the following w—yX

two mem˜ership fun™tions A1 —nd A2 for the input sp—™e x —nd two mem˜ership

fun™tions B1 —nd B2 for the input sp—™e y F gonsequently we get — systemD whi™h

is des™ri˜ed with four rules Ri : i = 1, . . . 4D in equ—tion TFQFQF „he output level

zi of e—™h rule is weighted ˜y the (ring strength wi of the ruleF „he (ring strength

is wi = T (A(x), B(y))F w—ny oper—tors T —re possi˜leD in this ™—se T is AN D

m—them—ti™—l oper—tionF

         R1 : If xi is A1 and yi is B1 then z1 = p1 xi + q1 yi + r1 .

         R2 : If xi is A1 and yi is B2 then z2 = p2 xi + q2 yi + r2 .

         R3 : If xi is A2 and yi is B1 then z3 = p3 xi + q3 yi + r3 .

         R4 : If xi is A2 and yi is B2 then z4 = p4 xi + q4 yi + r4 .

                                                                              @TFQFQA

where A(.), B(.) —re the mem˜ership fun™tions for snputs x —nd y F sn (gure TFT the

                        Layer 1   Layer 2        Layer 3   Layer 4
                                                 x, y

                          A1
                  X
                          A2
                                            A1
                                                              Z
                          A3
                  Y
                          A4

pigure TFTX qener—l ™onne™tion stru™ture of psƒ for xeuroEpuzzy modelD in ™—se of
four rules with line—r ™onsequentsF


neurons of every l—yer —re simil—r —nd h—ve the s—me spe™i(™ fun™tionF „he (rst one
          IPV                           TFH    €erform—n™es of proposed p„wg —lgorithm



is —d—ptive —nd ™—l™ul—te the mem˜ership degrees for di'erent mem˜ership fun™tionsD

whi™h su˜divides the ™orresponding input v—ri—˜le setF „he ™orresponding fun™tion

for every gbellmf @gener—lised ˜ellEsh—ped mem˜ership fun™tionA is given for x input

v—ri—˜le set —sX
                                                          1
                             output = µAi (x) =                                  @TFQFRA
                                                     1 + ( x−b )2c
                                                            a

where (a, b, and c)X —re p—r—meters setF

„he se™ond l—yer ™—l™ul—te the produ™t of —ll the in™oming sign—lsD e—™h neurone9s

output represents the (ring strength of its ruleX


                         output = wi = µAi (x) · µBi (y), i = 1, 2.              @TFQFSA


sn the third l—yer e—™h neuron h—s input v—ri—˜lesX xD y —nd θD θX is p—r—meters ve™torF

es output it gives the produ™t of norm—lised (ring strength wi —nd rules outputs zi

—sX
                                                      wi
                         output = wi zi =                       · zi .           @TFQFTA
                                              w1 + w2 + w3 + w4

sn ™—se of (rst order T akagiESugeno modelD the fun™tions zi , i = 1, . . , 4D h—ve the

following expressionX

                             zi = f (x, y, θ) = pi x + qi y + ri .               @TFQFUA

„he l—st l—yer unit ™—l™ul—tes the over—ll outputX

                                        w1 z1 + w2 z2 + w3 z3 + w4 z4
                        output = Zi =                                 .          @TFQFVA
                                            w1 + w2 + w3 + w4

ell p—r—meters of (gure TFT ™—n ˜e initi—lised using the prior knowledge —˜out the

systemF
TFQF xeuroEfuzzy systems                                                  IPW



6.3.2 Neuro-fuzzy systems optimisation


„he pre™edent se™tion tre—ted the gener—l neuro-fuzzy models —r™hite™tureF „his neuE

r—l —r™hite™ture needs ˜oth stru™ture —nd p—r—meters to ˜e designedD whi™h should ˜e

—˜le to des™ri˜e —nd model the ™orresponding re—l systemF yptimis—tion pro™edure

of the ˜uilded neuro-fuzzy model ™—n ˜e —™™omplished ˜y the optimis—tion of ˜oth

stru™ture —nd p—r—metersF ry˜rid Neuro-Fuzzy ƒystems —re under intensive investiE

g—tionsF ƒu™h —ttention to them is m—inly provoked ˜y the ™om˜in—tion of fuzzy sets

—nd rules initi—lis—tion using prior knowledge of systemD —nd —lso le—rning —lgorithms

derived from neur—l networks theoryF puzzy rules ™ont—in inform—tion gener—lly in r—E

di—l ˜—sis fun™tions @RBF A p—r—metersD the experts ™—n de(ne mem˜ership fun™tions

of input set —nd rules output p—r—meters @™onsequentsA to design fuzzy systemsF xeuE

r—l xetworks @N N A h—ve the t—sk to tr—in these p—r—meters for getting the optimised

modelEp—r—metersF ƒu™h neuro-fuzzy models h—ve gener—lly p—r—meters divided in

two p—rtsF „he (rst one is the inputEset p—r—metersD whi™h —re ™—lled —lso nonline—r

p—r—metersD these p—r—meters des™ri˜e the q—ussi—n fun™tionsF „he se™ond p—rt is

the outputEset p—r—metersD whi™h —re ™—lled —lso ™onsequent p—r—metersD ˜e™—use they

des™ri˜e the rules9 ™onsequentsF

wodel optimis—tion is the pro™ess to (nd p—r—meters setting —nd modelE—r™heti™tureD

whi™h le—d to the ˜est perform—n™esF …su—llyD this kind of pro˜lems is solved ˜y di'erE

ent te™hniques for modelEp—r—meters —nd modelE—r™heti™tureF „he (rst p—rt of optiE

mis—tion is ™—lled p—r—mitri™—l optimis—tionD it de—ls with only the modelEp—r—metersF

…su—llyD this type of optimis—tion is divided it self in two other optimis—tion typesX

the (rst type —re deriv—tiveE˜—sed optimis—tion methods like des™ent methods —nd
        IQH                         TFH   €erform—n™es of proposed p„wg —lgorithm



newton9s methodsD —nd the se™ond type —re non deriv—tiveE˜—sed optimis—tion methE

ods like qeneti™ elgorithms @GAA —nd ‚—ndom ƒe—r™h @RS AF „he se™ond p—rt of opE

timis—tion is ™—lled stru™tur—l optimis—tionD it de—ls with only the modelE—r™heti™tureF

…su—lly this p—rt tre—ts the sele™tion —nd proje™tion of fe—ture inputEve™torsD see se™E

tion SFRD —nd —lso de—ls with the input sp—™e p—rtitioning —nd ™lusteringF

e˜out the p—r—metri™—lEoptimis—tionD it is possi˜le to ™re—te m—ny hy˜rid —lgorithmsD

whi™h work together to de—l with input —nd output p—r—metersF w—ny hy˜rid —lgoE

rithms —re known —™tu—lly see ‘TVD QPD RWD RH“F



6.4 Notion of interpretability
„his se™tion des™ri˜es the proposed supervised ™l—ssi(™—tion —ppro—™hD puzzy „rimmed

we—n gl—ssi(™—tion @F T M C AF st ful(lls the tr—nsp—ren™y @interpret—˜ilityA of fuzzy

system —nd good —™™ur—™yD —nd —llows the ™ooper—tion ˜etween expert rules —nd inE

du™ed rulesF en initi—l fuzzy rules system is gener—ted using the st—tisti™9s trimmed

me—n method ‘IU“F „his method provides this —lgorithm — good initi—l v—lues of the

™enters —nd ˜—ses of the mem˜ership fun™tionsF sn this —ppro—™hD e—™h ™l—ss is ™lusE

tered independently from the other ™l—ssesD —nd is modeled ˜y the ™omponents of

g—ussi—n fun™tionsF ƒome of known initi—lis—tion methodsD su™h —s gridEtype p—rtiE

tioningD ˜uild — ™omplex —nd nonEinterpret—˜le initi—l models —nd the optimis—tion

le—rning steps ˜e™ome ™omput—tion—lly dem—nding —nd longF ƒt—tisti™9s trimmed

me—n method ™—n —void infrequent o˜serv—tions d—t— points —nd gives —n optim—l

model initi—lis—tionD whi™h needsD —fter th—tD only — few tr—inEepo™hs to re—™h the deE

sired level of perform—n™eF „hus it ™—n ˜e ™onsidered —s — r—pid modelEidenti(™—tion

development toolF
TFRF xotion of interpret—˜ility                                             IQI



„he ™l—ssi™—l fuzzy ruleE˜—sed ™l—ssi(erEmodels ™onsists of —n interpret—˜le ifEthen

fuzzy rulesD e—™h one des™ri˜ing one of some de(ned ™l—ssesF sn this se™tion the go—l

of study is not only to look for the ™l—ssi(™—tion —™™ur—™y ˜ut it fo™uses on the design

of interpret—˜le fuzzy rule ˜—sed ™l—ssi(erEmodelF „he p—r—meters of this ™l—ssi(erE

model —fter its optimis—tion should h—ve — physi™—l signi(™—n™e ™orresponding to the

re—l systemF „he notion of interpret—˜ility in system models ˜—sed on fuzzy logi™ is

primordi—lF „he interpret—˜ility of the p—r—meters in optimised neuro-fuzzy models

without some ™onstr—ints is not gu—r—nteedF ren™e re—l e'ort must ˜e m—de to keep

the tr—nsp—ren™y in rule p—r—metersF „he proposed fuzzy ™l—ssi(™—tion —lgorithm

@F T M C A to perform the iwqE˜—sed (ngerEmovements ™l—ssi(™—tion h—s some —dE

v—nt—ges likeX interpret—˜ilityD tr—nsp—ren™yD distinguish—˜le fuzzy setsD ™over—ge —nd

simpli™ityF st will ˜e ™omp—red with other known intelligent ™omput—tion—l methods

to ev—lu—te its perform—n™esF



6.4.1 Input fuzzy sets initialisation
sniti—l fuzzy rule ˜—seD se™tion TFQD is derived from n —v—il—˜le inputEoutput d—t— p—irs

@Xnf D Yn AD the input w—trix Xnf a ‘Xij “ D where i = 1, ..., n is num˜er of me—sured

s—mples —nd j = 1, ..., f is num˜er of fe—turesF pirstD proposed supervised F T M C

™l—ssi(™—tion methodD see our pu˜li™—tion ‘UQ“D extr—™ts initi—l fuzzy model from d—t—

set using st—tisti™—l trimmed me—n method to o˜t—in — set of initi—l rulesF ƒe™ondD

it —pplies optimis—tion —lgorithms to —d—pt its rules9 p—r—metersF sniti—l fuzzy model

™—n ˜e de(ned using ™entres —nd r—dius v—lues for di'erent ™l—ssesF por this t—sk the

me—n v—lue for e—™h fe—ture ve™tor Fj —nd e—™h ™l—ss k is ™—l™ul—ted without t—king

in ™onsider—tion the outlier s—mplesF Fj = Xij ( i = 1, ..., nk ) represents the fe—ture
        IQP                          TFH   €erform—n™es of proposed p„wg —lgorithm



of indi™es j for the ™l—ss Ck D where nk denotes the num˜er of s—mples for the ™l—ss

Ck F „he num˜er of ™l—sses is KD where k = 1, ..., K F „he num˜er of s—mples for —ll
                 K
™l—sses is n =   k=1   nk F sn short des™ription of this methodD e—™h fe—ture ve™tor of

m—trix @l—˜el for e—™h ™l—ssA in the m—trix Xnf is ordered from the sm—llest to l—rgest

v—lueD deleting — sele™ted num˜er of s—mples from e—™h end of the ordered listD —nd

then —ver—ging the rem—ining v—luesD see ex—mple (gure TFUF por this t—sk we h—ve




           pigure TFUX we—n of origin—l d—t— —nd me—n of trimmed d—t—F


to ™hoose the trimming per™ent—ge β D 1 − β denotes the per™ent—ge of v—lues deleted

from e—™h end of the ordered listD in this ™—se β aHFWF

„he me—n of e—™h fe—ture ve™tor Fj —nd for e—™h ™l—ss Ck is given —sX
                                                nk
                                           1
                                   Vjk   =            Xij                        @TFRFIA
                                           nk   1=1

„his me—n h—s —n extreme sensitivity to e—™h single outlierD hen™e there is — suspe™t to

t—ke the me—n ve™tor Vij —s — me—sure of ™entresF yutliers —re infrequent o˜serv—tions

d—t— pointsD whi™h do not —ppe—r to follow the ™h—r—™teristi™ distri˜ution of the rest
TFRF xotion of interpret—˜ility                                            IQQ



of d—t—F ƒt—tisti™i—ns h—ve proposed — trimmed me—n —s solution for this pro˜lemF

„he num˜er of s—mples th—t will ˜e deleted from ˜oth ends of the ordered l—˜el ve™tor

is given —sX

                            ndk = 2 × round(nk × (1 − β))                        @TFRFPA

round is matlab ™omm—ndX it rounds the elements to the ne—rest integerF

„his pro™edure lets us de(ne the ™oordin—tes of ™entres for the Ck ™l—sses in f multiE

dimension—l sp—™eF por f aPD the s—mples of e—™h ™l—ss ™—n ˜e delimited with ellipsesD

whi™h h—ve the —˜ove des™ri˜ed ™entres —nd r—dius on e—™h —xisF sn this ex—mpleD




           pigure TFVX „rimmed me—n methodE˜—sed groups delimit—tionF


(gure TFVD there —re three ™l—sses ™orresponding to three di'erent (nger movementsD

whi™h —re Xthum˜D pointer —nd middleF „he p—r—meters of e—™h ellipsoid will ˜e used

to gener—te the initi—l fuzzy setsF por this t—sk gener—lised mem˜ership fun™tionD

equ—tion TFRFIW is ™hosenF ren™e input fuzzy sets initi—lis—tionD using trimmed me—nE

˜—sed for these d—t— s—mplesD will h—ve the following p—rtitionD (gure TFWD of the input

sp—™eF sf zero order T akagiEsugeno model is ™hosenD then the ™onsequent p—r—meters
        IQR                         TFH   €erform—n™es of proposed p„wg —lgorithm




     pigure TFWX „rimmed me—n methodE˜—sed input fuzzy sets initi—lis—tionF


of this ™l—ssi(erEmodel —re independent from input v—ri—˜lesF

„his —ppro—™h ™—n (nd — good st—rting point in proximity of the glo˜—l minimumD

—nd ™onsequently the le—rningEtime of deriv—tiveE˜—sed optimis—tion methods will ˜e

shorterD only few epo™hs of tr—ining —re requiredF „his pro™edure —voids —lso the

˜ig ™h—nges in mem˜ership fun™tions overl—ppingD whi™h ™—n le—d to —n inversion of

fuzzy setsF „he initi—l inputEsp—™e p—rtition with this method ful(ls m—ny ™riteri— of

tr—nsp—ren™y —nd sem—nti™ properties ‘PR“ —nd ‘IS“F



   • ™over—geX the —ll entry sp—™e is ™overedF „h—t me—ns the model is —˜le to

     perform —n output for —ll input s—mplesF



   • sem—nti™ order rel—tionX we h—ve not inversion of fuzzy setsF
TFRF xotion of interpret—˜ility                                           IQS



6.4.2 Mathematical description
gonsider the ™ontinuousEtime nonline—r system of two inputs x, y —nd one output z

of dimension nF

x T = x 1 , x2 , . . . , x n

y T = y 1 , y2 , . . . , y n

i—™h input sp—™e is presented with two mem˜ership fun™tions in the following w—yX

two mem˜ership fun™tions A1 and A2 for the input sp—™e x —nd two mem˜ership

fun™tions B1 and B2 for the input sp—™e y F gonsequently we get — systemD whi™h

is des™ri˜ed with four rules Rr : r = 1, . . . 4D equ—tion TFRFQF „he output level zj

of e—™h rule is weighted ˜y the (ring strength wr of the ruleF „he (ring strength

is wr = T (A(x), B(y))F w—ny oper—tors T —re —v—il—˜leD in this ™—se T is AN D

m—them—ti™—l oper—tionF

           R1 : If xj is A1 and yj is B1 then z1 = p1 xj + q1 yj + r1 .

           R2 : If xj is A1 and yj is B2 then z2 = p2 xj + q2 yj + r2 .

           R3 : If xj is A2 and yj is B1 then z3 = p3 xj + q3 yj + r3 .

           R4 : If xj is A2 and yj is B2 then z4 = p4 xj + q4 yj + r4 .         @TFRFQA

where A(.), B(.)X —re the mem˜ership fun™tions for snputs x —nd y F „he glo˜—l output

of the system is the weighted —ver—ge of —ll rule outputsD ™omputed in equ—tion TFRFR

—sX
                                               wr (x, y)zj
                                       r=1,...,4
                               Z=                                               @TFRFRA
                                            r=1,...,4 wr

„he (rst order T akagiESugeno rule —r™hite™ture is shown in the following di—gr—mD

(gure TFIHF ‡here pi D qi —nd ri X —re the line—r p—r—meter setsF

„he (ring strength wr D r = 1, 2, 3, 4 of e—™h rule is given —s — T oper—tor fun™tion
           IQT                               TFH   €erform—n™es of proposed p„wg —lgorithm




                                                              B1       W1
                                   A1


                                                         B2            W2
                                   A1


                                                                       W3
                                        A2                    B1


                                                                       W4
                                        A2               B2




                                               X                   Y



      pigure TFIHX „wo inputs —nd four rules T akagiESugeno fuzzy inferen™e systemF

of the mem˜ership degreesX

                                  w1 = T [µA1 (x) , µB1 (y) ].

                                  w2 = T [µA1 (x) , µB2 (y) ].

                                  w3 = T [µA2 (x) , µB1 (y) ].

                                  w4 = T [µA2 (x) , µB2 (y) ].

where T X is the yper—tor fun™tionD in our ™—se it presents the AN D or produ™t operE

—torD —nd µAi(x) , µBi(y) X —re mem˜ership degreesF

„hen the over—ll output is expressed —s — line—r ™om˜in—tion of the ™onsequent p—E

r—metersD equ—tion TFRFSX

                                    w1 z1 + w2 z2 + w3 z3 + w4 z4
                               Z=                                                    @TFRFSA
                                        w1 + w2 + w3 + w4

orD

                                                                            wr
                 Z = w1 z1 + w2 z2 + w3 z3 + w4 z4 . with wr =                       @TFRFTA
                                                                       r=1,4 (wr )
TFRF xotion of interpret—˜ility                                         IQU



6.4.3 Parameters identication
fy o˜serving inputEoutput d—t— p—irs of nonline—r physi™—l phenomenon it is possi˜le

to ˜uild — m—them—ti™—l model with —d—pted p—r—metersD whi™h ™—n identify our re—l

systemF „he purposes of system identi(™—tion ™—n ˜eX —pproxim—tionD modelling ‘RR“

or ™l—ssi(™—tion ‘SP“F

„he following (gure shows — s™hem—ti™ di—gr—m of re—l system identi(™—tion where

outputs Z —nd Z ∗ —re ˜oth system —nd model outputs respe™tivelyF „he identi(ed

m—them—ti™—l model should ˜e upd—ted till the —™™ept—˜le di'eren™e me—sure D =

Z − Z ∗ is re—™hedD (gure TFIIF sn se™tion TFRFP the ™ontinuousEtime nonline—r system

                    X                                            Z*
                              Real system to be identified

                                                             Z
                                      Builded Model




                                  Identification procedure
                                                             Z* - Z


       pigure TFIIX ƒ™hem—ti™ di—gr—m for m—them—ti™—l model identi(™—tion


of two inputs x, y —nd one output Z of dimension n is des™ri˜ed in the following

m—them—ti™—l modelDTFRFU


                           Z = w1 z1 + w2 z2 + w3 z3 + w4 z4 .                @TFRFUA


„he stru™ture of this model is —lre—dy de(ned empiri™—llyD this stru™ture in fuzzy

inferen™e system is determined ˜y —n expert who h—s enough knowledge —˜out the

re—l systemF „here —re m—ny methodsD whi™h help us to de(ne the num˜er of MFs
        IQV                             TFH    €erform—n™es of proposed p„wg —lgorithm



—nd rulesD su™h —s ™lustering methodsF xow it rem—ins only the optimis—tion of

model p—r—metersF „his model is ™omposed of two p—r—meter setsD (rst —re the

nonline—r p—r—meters of the mem˜ership fun™tionsD A1 D A2 D B1 D —nd B2 F ƒe™ond

the line—r p—r—meters of the ™onsequent rulesD pi , qi and ri , i = 1, 2, 3, 4F „o

illustr—te identi(™—tion methods for these two types of p—r—metersD this study will

˜e divided in two p—rtsD (rst identi(™—tion of line—r p—r—meters with ™onsider—tion

th—t the nonline—r p—r—meters —re ™onst—ntD —nd se™ond identi(™—tion of nonline—r

p—r—meters with ™onsider—tion th—t the line—r p—r—meters —re ™onst—ntF


a) Linear parameters identication

„he expressions of the fun™tions z1 , z2 , z3 , and z4 in equ—tion TFRFU —re introdu™ed

to get the following equ—tion TFRFV

           zj = w1 ( p1 xj + q1 yj + r1 ) + w2 ( p2 xj + q2 yj + r2 )

              +w3 ( p3 xj + q3 yj + r3 ) + w4 ( p4 xj + q4 yj + r4 ).

orD

       zj = (w1 xj )p1 + (w1 yj )q1 + (w1 )r1 + (w2 xj )p2 + (w2 yj )q2 + (w2 )r2

         +(w3 xj )p3 + (w3 yj )q3 + (w3 )r3 + +(w4 xj )p4 + (w4 yj )q4 + (w4 )r4    @TFRFVA

„his l—st equ—tion TFRFV ™—n ˜e formul—ted in the following new equ—tion TFRFW

                   zj = f1 (xj , yj )p1 + f2 (xj , yj )q1 + f3 (xj , yj )r1

                       +f4 (xj , yj )p2 + f5 (xj , yj )q2 + f6 (xj , yj )r2

                       +f7 (xj , yj )p3 + f8 (xj , yj )q3 + f9 (xj , yj )r3

                    +f10 (xj , yj )p4 + f11 (xj , yj )q4 + f12 (xj , yj )r4         @TFRFWA
TFRF xotion of interpret—˜ility                                                                          IQW



fm (xj , yj )X —re the known fun™tions of our input ve™tor p—irs {xj , yj }D where mX

represents the num˜er of line—r p—r—metersF

pin—lly the output Z in equ—tion TFRFW des™ri˜es —n output of — line—r modelD whi™h

is gener—lly given ˜y the line—rly p—r—meterised expressionD equ—tion TFRFIH

                         Z = f1 (u)θ1 + f2 (u)θ2 + . . . + fm (u)θm                                             @TFRFIHA

where f1 , . . ., fm X —re known fun™tions of u = [u1 , . . ., uj ]T , uj = {xj , yj }D —nd

θ1 , . . ., θm X —re unknown p—r—metersF

sn equ—tion TFRFW the line—r p—r—meters —re pi , qi and ri , i = 1, 2, 3, 4F st is

™onsidered th—t there —re n me—sured d—t— p—irs [(xj , yj ); zj ] of the re—l systemD

where j = 1, . . ., nF yur identi(ed model is presented in these following n line—r

equ—tions TFRFIIX




 z1 = f1 (u1 )p1 + f2 (u1 )q1 + f3 (u1 )r1 + . . . + f10 (u1 )p4 + f11 (u1 )q4 + f12 (u1 )r4 ,

 z2 = f1 (u2 )p1 + f2 (u2 )q1 + f3 (u2 )r1 + . . . + f10 (u2 )p4 + f11 (u2 )q4 + f12 (u2 )r4 ,

                      ..............................................................................................,

                      ..............................................................................................,

zn = f1 (un )p1 + f2 (un )q1 + f3 (un )r1 + . . . + f10 (un )p4 + f11 (un )q4 + f12 (un )r4 ,

                                                                                                                @TFRFIIA

sn m—trix formD the pre™edent equ—tions ™—n ˜e written —sX

                                                  MΘ = Z                                                        @TFRFIPA

where M is — m—trix of dimension n × mX
          IRH                               TFH    €erform—n™es of proposed p„wg —lgorithm


                                                                         
                                        f1 (u1 ) . . .        f12 (u1 )
                                                                     
                                       .           .             .   
                                   M =
                                                                     
                                                                      
                                       .           .            . 
                                                                     
                                       f1 (un ) . . .        f12 (un )

Θ is — ve™tor of unknown line—r p—r—meters of dimension 1 × m = 12 to ˜e identi(edX

                     Θ = [p1 , q1 , r1 , p2 , q2 , r2 , p3 , q3 , r3 , p4 , q4 , r4 ]T

Z is —n output ve™tor of dimension 1 × nX

                                      Z = [z1 , z2 , ., ., ., zn ]T

„o identify this unknown nonline—r p—r—meters ve™tor it is ne™ess—ry th—t the me—E

sured d—t— p—irs dimension of the systemD should ˜e gre—ter th—n unknown p—r—meters

dimension of its identi(ed modelF „his ™ondition is veri(ed in this ™—se @n ≥ 12DAF sf

M is squ—re —nd nonsingul—r @its determin—nt is nonzeroAD then it is possi˜le to solve

the equ—tionX M Θ = Z D —sX

                                              Θ = M −1 Z                                  @TFRFIQA

…nfortun—tely there is —lw—ysD in re—l systemsD — di'eren™e ˜etween the me—sured re—l

system response Z ∗ —nd the identi(ed m—them—ti™—l system responseF „his di'eren™e

™—n ˜e des™ri˜ed —s the error e due to m—ny extern—l f—™tors non identi(edF „hen to

represent the re—l output responseD the error —mong e will ˜e —dded in the following

w—yX

                                            M Θ + e = Z∗                                  @TFRFIRA

por e—™h me—sured d—t— p—irs [(xj , yj ), zj ], j = 1, . . . , nD the error ej is given —sX ej =

zj − zj (pi , qi , ri ) = zj ∗ −
 ∗                                           T
                                    m=1,12 [Mjm   Θm ]D j = 1... nD i = 1... 4D —nd m = 1, ..., 12F

„he sum of squ—red error of the error ve™tor e(Θ) = [e1 , . . . , en ]T represents the
TFRF xotion of interpret—˜ility                                             IRI



error in our identi(ed model responseF „his error is o™™urred in estim—ting unknown

line—r p—r—meters ve™tor ΘD hen™e the sum of squ—red error is sym˜olised —s E(Θ)X


                    E(Θ) =         (zj ∗ −            [Mjm Θm ])2 = eT e.
                                                        T
                                                                                  @TFRFISA
                             j=1,n           m=1,12

sn m—trix formD the pre™edent equ—tion ™—n ˜e written —sX


                        E(Θ) = (Z ∗ − M Θ)T (Z ∗ − M Θ).                          @TFRFITA


„he sum squ—red errorD E(Θ)D de(ned in equ—tion TFRFIS is depending on the v—lues of

the unknown line—r p—r—meters of ve™tor ΘF „he ˜est p—r—meter v—lues of this ve™tor

ΘD whi™h is designed —s Θ∗ ™orresponding to the minimum v—lue of sum squ—red error

E(Θ)F

…sing ve—st ƒqu—res istim—tor @LSE A method ‘TQ“ it is possi˜le to solve the pre™edent

equ—tion TFRFIT to re—™h this optim—l solution Θ = Θ∗ D whi™h s—tis(es the norm—l

equ—tionX

                                  M T M (Θ∗ ) = M T Z.                            @TFRFIUA

sf M T M is nonsingul—rD then the optim—l solution Θ∗ is uniqueX


                                  Θ∗ = [M T Z]−1 M T Z.                           @TFRFIVA



b) Nonlinear parameters identication

„he ™—se of gener—lised ˜ellEsh—ped mem˜ership fun™tion for the mem˜ership fun™E

tionsD A1 D A2 D B1 —nd B2 D (gure TFIHD is ™onsideredF „hese fun™tions —re de(ned

—sX
                                                       1
                             A1,2 (x) =                                           @TFRFIWA
                                          1+    ( x−b11,12 )2c11,12
                                                   a11,12
           IRP                              TFH    €erform—n™es of proposed p„wg —lgorithm



—nd
                                                             1
                                   B1,2 (y) =                                                @TFRFPHA
                                                  1+   ( y−b11,12 )2c11,12
                                                          a11,12

„he nonline—r p—r—meters of ve™tor Ω for these four mem˜ership fun™tions —re given

respe™tively —sX


          Ω = [a11 , b11 , c11 , a12 , b12 , c12 , a21 , b21 , c21 , a22 , b22 , c22 ]T      @TFRFPIA


sn this ™—se these p—r—meters —re ™onsidered unknownD —nd the line—r p—r—meters

ve™torD Θ = [p1 , q1 , r1 , p2 , q2 , r2 , p3 , q3 , r3 , p4 , q4 , r4 ]T is ™onsidered knownF Ω

is — ve™tor of unknown nonline—r p—r—meters of dimension 1 × m = 12 @the s—me

dimension —s line—r p—r—metersAF ƒin™e the mem˜ership fun™tions —re ™ontinuous —nd

di'erenti—˜leD the ˜—si™ le—rning ruleD whi™h is the simple steepest des™ent method

dis™ussed in se™tion TFPFQ is —ppliedF vike m—nner —s for line—r p—r—metersD the error

e(Ω) = [e1 , . . . , en ]T represents the error in our identi(ed model responseF „his

error is o™™urred in estim—ting unknown nonline—r p—r—meters of ve™tor ΩD hen™e the

sum of squ—red error is sym˜olised —s E(Ω)X


      E(Ω) = E([a11 , b11 , c11 , a12 , b12 , c12 , a21 , b21 , c21 , a22 , b22 , c22 ]T )   @TFRFPPA


por e—™h me—sured d—t— p—irs [(xj , yj ), zj ], j = 1, . . . , nD the error ej is given —sX

ej = zj − zj (ast , bst , cst ), st = 11, 12, 21 and 22F
      ∗


where zj X is the me—sured outputD —nd zj (ast , bst , cst )X is the output of the ˜uilded
       ∗


modelF „he gr—dientE˜—sed optimis—tion method des™ri˜ed in se™tion TFPFQ ™—n ˜e

—pplied to identify e—™h p—r—meter of the ve™tor ΩF yur o˜je™tive fun™tion is E(Ω)F

sn iter—tive des™ent methodD like steepest des™entD the next v—luesD Ωnext D of the ve™tor

Ω is determined using — le—rning r—te 4step down4 —nd the ™urrent point Ωnow in the
TFRF xotion of interpret—˜ility                                                          IRQ



dire™tion of the gr—dient g X

                                         Ωnext = Ωnow − ρg                                     @TFRFPQA


where ρX represents — le—rning r—teF

gX   is — gr—dient ve™tor th—t moves tow—rds — lo™—l minimum Ω∗ of our o˜je™tive fun™E

tion E X    n
                →



     Parameters identication of vector Ω:
sn the equ—tion TFRFIWD the gener—lised ˜ellEsh—ped mem˜ership fun™tion @gbellmf A

A1 h—s three unknown p—r—metersD whi™h —reX a11 , b11 , and c11 F „he identi(™—tion of

e—™h of them is given —sX

                                                                      ∂ej
                         (a, b, c)11,next = (a, b, c)11,now − ρ                                @TFRFPRA
                                                                   ∂(a, b, c)11

                       ∂ej                                      ∂zj (ast , bst , cst )
                                     ∗
                                 = (zj − zj (ast , bst , cst ))                                @TFRFPSA
                    ∂(a, b, c)11                                   ∂(a, b, c)11

sf the equ—tion TFRFS is ™onsideredD then we getX

                                                                    r=4
                         ∂zr (ast , bst , cst )        ∂            r=1 wr zr
                                                =              (     r=4      ),               @TFRFPTA
                            ∂(a, b, c)11          ∂(a, b, c)11       r=1 wr


where rX num˜er of rulesF




remark: don't confuse between zj , which is the measured system output and zr , which

represents the only rules' conclusion.


purther ™omput—tions of equ—tion TFRFPT le—d to (n—l deriv—tive results of A1 (x) with
         IRR                            TFH   €erform—n™es of proposed p„wg —lgorithm



respe™t to p—r—meters (a, b, c)11 —sX

                             ∂A1 (x)    2c11
                                     =       · (1 − A1 (x)) · A1 (x)              @TFRFPUA
                              ∂a11      a11
                       ∂A1 (x)    2c11 x − b11 2c11 −1
                               =      ·(          )       · (A1 (x))2             @TFRFPVA
                        ∂b11      a11       a11
                      ∂A1 (x)             x − b11 2c11 −1
                              = −2c11 · (         )       · (A1 (x))2             @TFRFPWA
                       ∂c11                 a11
sn the s—me w—yD the (n—l deriv—tive results of A2 (x) with respe™t to the p—r—meters

(a, b, c)12 is given —sX
                             ∂A2 (x)    2c12
                                     =       · (1 − A2 (x)) · A2 (x)              @TFRFQHA
                              ∂a12      a12
                       ∂A2 (x)    2c12 x − b12 2c12 −1
                               =      ·(          )       · (A2 (x))2             @TFRFQIA
                        ∂b12      a12       a12
                      ∂A2 (x)             x − b12 2c12 −1
                              = −2c12 · (         )       · (A2 (x))2             @TFRFQPA
                       ∂c12                 a12
„he (n—l deriv—tive results of B1 (y) with respe™t to the p—r—meters (a, b, c)21 is given

—sX

                             ∂B1 (y)    2c21
                                     =       · (1 − B1 (y)) · B1 (y)              @TFRFQQA
                              ∂a21      a21
                       ∂B1 (y)    2c21 y − b21 2c21 −1
                               =      ·(          )       · (B1 (y))2             @TFRFQRA
                        ∂b21      a21       a21
                      ∂B1 (y)             y − b21 2c21 −1
                              = −2c21 · (         )       · (B1 (y))2             @TFRFQSA
                       ∂c21                 a21
et the end the (n—l deriv—tive results of B2 (y) with respe™t to the p—r—meters (a, b, c)22

is given —sX

                             ∂B2 (y)    2c22
                                     =       · (1 − B2 (y)) · B2 (y)              @TFRFQTA
                              ∂a22      a22
                       ∂B2 (y)    2c22 y − b22 2c22 −1
                               =      ·(          )       · (B2 (y))2             @TFRFQUA
                        ∂b22      a22       a22
                      ∂B2 (y)             y − b22 2c22 −1
                              = −2c22 · (         )       · (B2 (y))2             @TFRFQVA
                       ∂c22                 a22
TFRF xotion of interpret—˜ility                                            IRS



6.4.4 Complexity and interpretability consideration in both
      FSC and FTMC models

„wo iwq surf—™e ele™trodes —re pl—™ed on two mus™le groupsD palnaris longus @channel1 A

—nd extensor digitorum @channel2 AD the lo™—tions of ele™trodes on the su˜je™t9s —rm

is given in (gure TFIPF prom the input fe—ture sp—™eD the ™l—ssi(er must ˜e —˜le

to ™l—ssify the three output ™l—sses exploiting the inform—tion in iwq sign—l me—E

surementsF por e—™h ™h—nnel the sign—l w—s re™orded using — single ˜ipol—r surf—™e

ele™trode p—irF „he sign—l w—s s—mpled —t — r—te of 4Khz using A/D ˜o—rd in —n IBM




   pigure TFIPX ‚e™ording of iwq sign—ls using two p—irs of surf—™eEele™trodes


PC/AT ™omp—ti˜le mi™ro™omputerF „his —lgorithm is developed with M AT LAB 6.5

—nd is performed in — €gE˜—sed o'Eline pro™essF „he hum—n su˜je™t w—s —sked to

produ™e — num˜er of ™ontinuous movementsD QR single ™ontr—™tion periods —re sep—E

r—ted from the ™orresponding sets of ™ontinuous movementsF sniti—l 400ms sign—l p—rt

of e—™h single ™ontr—™tion period is extr—™ted from the r—w sign—l ™onsidering de(ned

threshold rel—tive to noise st—nd—rdEdevi—tion v—lueD see se™tions RFP —nd UFQF „hese

extr—™ted sign—ls —re —n—lysed using ƒhort „ime pourier „r—nsform @ST F T AF „his

—n—lysis method gives — me—sure of ˜oth time —nd frequen™y inform—tion for short

sign—l segmentsD see se™tion RFRFRF

ixtr—™tion of relev—nt fe—turesD see se™tion RFRFRF™D needs the use of spe™trum —n—lysis

˜—sed timeEfrequen™y dom—inF „imeEfrequen™y —n—lysis ˜—sed on shortEtime pourier
         IRT                        TFH     €erform—n™es of proposed p„wg —lgorithm



tr—nsform @ST F T AD is — form of lo™—l pourier —n—lysis th—t shows the ™h—nges of power

spe™tr—l density @P SDA of iwq sign—ls during timeF „his method le—ds to — ˜etter

solution to design fe—ture extr—™tionD see se™tion RFRFRF™F „he nth order of frequen™y

moment distri˜ution —t time t is de(ned —sX


                             Mn (t) =        n
                                            ωk |ST F T (t, k)|                  @TFRFQWA
                                        k


where Mn (t)X is the nth moment of the frequen™y distri˜ution —t time tD nX order —nd

ω X frequen™yF

…sing two ™h—nnelsD some iwq tr—ining —nd test d—t—D from (ltered r—w iwq sign—l

˜etween 30Hz —nd 250Hz —re prep—red see se™tions RFQFI —nd UFPF „hree ™l—sses

l—˜elled ID P —nd Q h—ve SI tr—inEs—mples —nd SI testEs—mplesF „he distri˜ution of

—ll s—mples in Ph dimension—l sp—™eD Channel1 —nd channel2 D is shown in (gure TFIQF

elso tr—in —nd test s—mples distri˜ution is presented in (gure TFIRF




                      pigure TFIQX qlo˜—l s—mples distri˜ution
TFRF xotion of interpret—˜ility                                              IRU




                  pigure TFIRX „r—in —nd test s—mples distri˜utionF


a) FTMC fuzzy classier-model

„he s—mples of e—™h ™l—ss for these —ll tr—in —nd test d—t—D (gure TFIQD ™—n ˜e delimitedD

—™™ording to trimming per™ent—ge β = 0.9F these delimit—tions —re done with ellipses

using des™ri˜ed „rimmed we—n snisi—lis—tion method @T M I AD see se™tion TFRFIF heE

rived ellipses for only tr—in s—mples —re presented in (gure TFISF „he p—r—metersD




pigure TFISX illipses derived from               pigure TFITX snput fuzzy sets initi—liE
TMI —lgorithm for tr—inEs—mplesF                 s—tion using FTMC —lgorithmF
        IRV                          TFH   €erform—n™es of proposed p„wg —lgorithm



™entres —nd r—diusD of e—™h ellipsoid will ˜e used to gener—te the initi—l fuzzy setsF

por this t—sk the gener—lized ˜ell mem˜ership fun™tion is ™hosenF illipsoidsE˜—sed

input fuzzy sets initi—lis—tion for tr—in d—t—D whi™h gives us the p—rtition of our inE

put tr—inEs—mples sp—™e is presented in (gure TFITF xowD —fter using „rimmed we—n

snisi—lis—tion method @T M I AD it is possi˜le to ˜uildD from d—t—D — ™omp—™t fuzzy ™l—sE

si(er rules with singleton ™onsequents to get zeroEorder „FƒF modelF sn this method

the num˜er of rules to ˜e gener—ted needs to ˜e determinedD a prioriD whi™h —re in

this ™—se three rules ™orresponding to our three ™l—ssesF „his ˜uilded fuzzy model h—s

three mem˜ership fun™tions for e—™h inputF „he singleton output ™onsequents of this

model use the following ™l—ssi(™—tion rulesD   TFRFRH
                                  
                                   1 if
                                              Zk < 1, 5
                                  
                       Classk =      2 if      1, 5 ≤ Zk < 2, 5                 @TFRFRHA
                                  
                                   3 if
                                  
                                               Zk ≥ 2, 5
„he input fuzzy set p—r—meters of the initi—l modelD (gure TFITD —re given in t—˜le

TFPF „his initi—l model with three rulesD whi™h des™ri˜es Q ™l—sses with singleton ™onE

„—˜le TFPX Gbellmf mem˜ership fun™tions €—r—meters of initi—l fuzzy F T M C
™l—ssi(erEmodel
                  snput I gbellmf p—r—meters pun™tions
                       A1        HFQSI HFUHP EHFWRT     gbellmf A1
                       A2        HFQPR HFTRU EHFPVS     gbellmf A2
                       A3        HFWTH IFWPI IFRTQ      gbellmf A3
                     snput P    g˜ellmf p—r—meters       pun™tions
                        B1       IFSIH QFHPH HFQIW      gbellmf B1
                        B2       IFITW PFQQU EHFQIT     gbellmf B2
                        B3       IFIPP PFPRR HFSPW      gbellmf B3


sequentsD h—s —ver—ge ™l—ssi(™—tion —™™ur—™y of VHFQWPP% giving 4IH4 mis™l—ssi(ed

s—mples on the test d—t—D (gure TFIUF ‡ith more det—iled studyD it is possi˜leD not
TFRF xotion of interpret—˜ility                                            IRW




     pigure TFIUX wis™l—ssi(ed s—mples of initi—l fuzzy F T M C ™l—ssi(erEmodel



onlyD to lo™—te the glo˜—l mis™l—ssi(ed s—mples for —ll three ™l—ssesD ˜ut —lso the misE

™l—ssi(ed s—mples for e—™h ™l—ssF por the (rst ™l—ssD thum˜ (nger )exionD there —re 4Q4

mis™l—ssi(ed s—mples @ VPFQSPW%AD whi™h —re ™l—ssi(ed —s pointer (nger movementF

e˜out the se™ond ™l—ssD pointer (nger )exionD there is only 4I4 mis™l—ssi(ed s—mpleD

or WRFIIUT% ™orre™tD whi™h is ™l—ssi(ed —s thum˜ (nger movementF „he third ™l—ssD

middle (nger )exionD h—s 4T4 mis™l—ssi(ed s—mplesD or TRFUHSW % ™orre™tD whi™h —re

™l—ssi(ed —s pointer (nger movementF

efter gener—ting the initi—l T M I p—rtitioning of input sp—™e using F T M C E™l—ssi(er


modelD the following —d—pt—tion method is —pplied to perform —nd in™re—se the reE

sults —™™ur—™y of this ™l—ssi(erEmodelF „his optimis—tion is done in two stepsX the

(rst one is optimis—tion of premise p—r—meters @mem˜ership fun™tions p—r—metersA

using qr—dient hes™ent @GDAD see se™tion TFRFQF˜F „he se™ond step is the optimis—tion
        ISH                         TFH   €erform—n™es of proposed p„wg —lgorithm



of the line—r p—r—meters @gonsequen™e p—r—metersA using line—r ve—st ƒqu—res istiE

m—tor @LSE AD see se™tion TFRFQF—F sniti—l proposed F T M C ™l—ssi(™—tion —lgorithmD

des™ri˜ed —˜ove h—s found — good st—rting point in proximity of the glo˜—l minimumD

whi™h h—d — ™l—ssi(™—tion —™™ur—™y equ—l to VHFQWPP%F ren™e we expe™t th—t the

—d—pt—tion of this initi—l model will need the —ppli™—tion of only — few optimis—tion

epo™hs —nd ™onsequently will not h—ve — ˜ig e'e™t on the overl—p of mem˜ership

fun™tions —nd —lso will not ˜e timeE™onsumingF „he optimis—tionD during only four

epo™hsD of our initi—l F T M C E™l—ssi(er modelD (gure TFITD on ˜oth —nte™edents —nd

™onsequents p—r—meters using GD —nd LSE respe™tivelyD gives — new rep—rtition of

input sp—™eF „his rep—rtition is presentedD with gbellmf mem˜ership fun™tionsD in

(gure TFIVF „hese new optimised fun™tions don9t present — ˜ig di'eren™e in ™omp—rE




        pigure TFIVX Gebellmf fun™tions —fter R epo™hs F T M C optimis—tion


ison with their initi—l fun™tionsF ren™e the ƒem—nti™ order rel—tion @no inversion of

fuzzy setsA see se™tion TFRFID is ™onservedF ‡e o˜t—in ™onsequently the new ™l—ssi(™—E

tion —™™ur—™y equ—l to VVFPQSQ% giving T s—mples of mis™l—ssi(™—tionD they were 4IH4
TFRF xotion of interpret—˜ility                                           ISI



˜efore optimis—tion on the d—t— test see (gureD TFIWF st is possi˜le —lso to lo™—te the




      pigure TFIWX wis™l—ssi(ed s—mples of optimised F T M C ™l—ssi(erEmodel


glo˜—l mis™l—ssi(ed s—mplesD —fter optimis—tionD for —ll these three ™l—ssesD —nd the

mis™l—ssi(ed s—mples for e—™h ™l—ssF por the (rst ™l—ss @thum˜ (nger )exionA there

—re 4Q4 mis™l—ssi(ed s—mplesD or VPFQSPW%D whi™h —re ™l—ssi(ed —s pointer (nger )exE

ionF e˜out the se™ond ™l—ssD pointer (nger )exionD —ll s—mples —re ™l—ssi(ed ™orre™tly

@IHHFH% ™orre™tAF „he third ™l—ssD middle (nger )exionD h—s 4Q4 mis™l—ssi(ed s—mplesD

or VPFQSPW % ™orre™tD whi™h —re ™l—ssi(ed —s pointer (nger movementF

„he ™orresponding rules to the new input fuzzy sets of optimised F T M C ™l—ssi(erE

model —nd their singleton output ™onsequents —re given in equ—tion TFRFRIF
             
              1 if x is A1 —nd y is B1 then Zk = 0.686 < 1, 5
             
             
    Classk =   2 if x is A2 —nd y is B2 then 1, 5 ≤ Zk = 2.305 < 2, 5           @TFRFRIA
             
              3 if x is A —nd y is B then Z = 3.173 ≥ 2, 5
             
                          3           3        k


ell optimised p—r—metersD nonline—r p—r—meters —nd line—r p—r—metersD ˜elong to the

de(ned dom—inEsp—™e of the re—l systemF „here is interpret—˜ility —nd tr—nsp—ren™y
        ISP                         TFH   €erform—n™es of proposed p„wg —lgorithm



for the o˜t—ined optimised fuzzy F T M C ™l—ssi(erEmodelF sts p—r—meters v—lues h—ve

— ™le—r physi™—l me—ningF




b) Fuzzy subtractive clustering (FSC )

„he su˜tr—™tive ™lustering —lgorithm is proposed ˜y Chiu @IWWRAF st estim—tes the

num˜er of ™lusters —nd the ™luster ™entres in — set of d—t— ˜y —n iter—tive pro™edureF

„he ™lusters o˜t—ined —re used to initi—lise the fuzzy setsD for AN F IS EmodelF „he

resultsD model perform—n™es —nd the notion of interpret—˜ilityD will ˜e ™omp—red with

those of our —llgorithmF „he M atlab ™omm—nd genf is2D in fuzzy logi™ tool˜ox to genE

er—te the initi—l model with su˜tr—™tive ™lusteringD uses the (rst order T akagiESugeno

@T.S.A modelF efter AN F IS optimis—tion methodD (gure TFPHD the ™l—ssi(™—tion —™™uE

r—™ies for di'erent epo™hsX SD PH —nd SH epo™hsD —re equ—l to VTFPURS% VVDPQSQ% —nd

WHFIWTI% giving UD T —nd S mis™l—ssi(ed s—mples respe™tively on the d—t— testF „he




pigure TFPHX AN F IS yptimis—tion of input fuzzy sets for ƒu˜tr—™tive glustering
@FSC A method
TFRF xotion of interpret—˜ility                                             ISQ



o˜t—ined fuzzy model with ƒu˜tr—™tive ™lustering method h—sn9t — physi™—l me—ning

—nd is not interpret—˜leD equ—tion TFRFRPF „he ™onsequent p—r—meters of the (ve rules

in optimised (rst   order 4T.S.4 model —re given in equ—tion TFRFRPF
            
             1
            
                   if x is A1 —nd y is B1 then Zk = −1.521 0.6723 2.014
            
                    if x is A2 —nd y is B2 then Zk = −1.081 0.3386 − 0.215
            
             2
            
            
            
  Classk =     3    if x is A3 —nd y is B3 then Zk = −0.0390 0.0102 3.072         @TFRFRPA
            
                    if x is A3 —nd y is B3 then Zk = 0.7526 − 0.1067 1.76
            
             4
            
            
            
            
             5     if x is A3 —nd y is B3 then Zk = −2.512 1.537 3.805
            

sn the following t—˜le TFQD some ™h—r—™teristi™s of ˜oth methodsD F SC —nd F T M C D

—re resumed in ™omp—rison formF F

      „—˜le TFQX F SC —nd F T M C ™l—ssi(erEmodels ™h—r—™teristi™s ™omp—rison
                                    yur —ppro—™h ƒu˜F glustering
                    wfF „ypF           Gbellmf         Gaussmf
               x˜F puzzy sets snEI            Q                S
               x˜F puzzy sets snEP            Q                S
                 x˜ €—rmtrF sn               IV               PH
                gonsequent typF          ƒingleton          line—r
                x˜ €—rmtrF yut                Q               IS
                   x˜F of rules               Q                S
                 snterpret—˜ility           yes               no
                „r—ining@epo™hsA              R               PH
                  e™™ur—™y@%A             VVDPQSQ          VVDPQSQ




6.4.5 Conclusion
„he proposed fuzzy ™l—ssi(™—tion —lgorithmD to perform the iwq sign—lsE˜—sed (ngerE

movements ™l—ssi(™—tionD h—s sever—l —dv—nt—ges th—t motiv—te the use of fuzzy sysE

tems likeX interpret—˜ilityD tr—nsp—ren™yD distinguish—˜le fuzzy setsD ™over—ge —nd simE

pli™ityF „his —lgorithm extr—™t fuzzy rules from me—sured re—l system d—t— setD whi™h
         ISR                        TFH   €erform—n™es of proposed p„wg —lgorithm



use trimmed me—n me—sure to —void infrequent o˜serv—tions d—t— pointsF st gives —n

optim—l model initi—lis—tionD whi™h needs —fter th—t only R tr—inEepo™hs to re—™h the

s—me perform—n™e —s with F SC D whi™h needs PH epo™hsF

e f—st —nd pr—™ti™—l method for ™l—ssi(™—tion with — simpli(ed fuzzy ™l—ssi(erEmodel

is developedF „he stru™ture —nd p—r—metersD of this proposed fuzzy F T M C ™l—ssi(erE

modelD —re simult—neously optimizedF woreover this model does not loss its interE

pret—˜ilityF



6.5 Comparison btween MLP, RBF, LVQ and FTMC
„hree intelligent ™omput—tion—l —lgorithms will ˜e used to perform the ™l—ssi(™—tion

of — new ™onsidered re—l systemD whi™h is — dis™rimin—tion of four di'erent h—nd

movements —™™ording to their ™orresponding iwq sign—lsF sntelligent ™omput—tion—l

—lgorithms used in this se™tion —re those ˜—sed on neur—l networks —nd neuroEfuzzy

networks like wultiEv—yer €er™eptron @M LP AD ‚—di—l f—sis xetworks @RBF A —nd

ve—rning †e™tor u—ntiz—tion network @LV QAF „he purpose of this se™tion is to illusE

tr—te these v—rious intelligent ™omput—tion—l —lgorithms —nd to ™omp—re them with

the perform—n™e of proposed F T M C fuzzy ™l—ssi(erE—lgorithmD see our pu˜li™—tion

‘UQ“F iwq sign—l preEpro™essing oper—tionD see se™tion RFRFRD is performed using spe™E

trum —n—lysis ˜—sed on ƒhort „ime pourier „r—nsform @ST F T AF ‡ith this method it

is possi˜le to exploit —nd to qu—ntify the ˜eh—viour of dyn—mi™ inform—tion presented

in iwq sign—ls —nd to design ™h—r—™teristi™ @fe—tureA ve™torsF „hese ve™tors ™—n

perform — relev—nt fe—tures th—t le—d to — good dis™rimin—tion of these four di'erent

™l—sses of h—nd movementsF „he fun™tionD whi™h des™ri˜es the se™ond order momentD

@M2 AD is used —s fe—ture for the further dis™rimin—tion t—skF „he de(nition of this
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                             ISS



fun™tion is given in equ—tion TFRFQW se™tion TFRFRF



6.5.1 Proposed FTMC classier-model
a) Initial fuzzy (FTMC ) classier-model




              pigure TFPIX qlo˜—l s—mples distri˜ution of fe—ture M 2F


   ƒin™e —ll tr—ining —nd test d—t— in the ™—se of woment of se™ond order fe—ture @M2 A

—re prep—redD (gures TFPI —nd TFPPD the —™™ur—™y of fuzzy F T M C ™l—ssi(erEmodel —™E

™ording to trimming per™ent—ge β = 0.9 will ˜e performedF „he ™lusters @ellipsesA

derived from T M C —lgorithm for the tr—ining s—mples of e—™h ™l—ss sn 2D sp—™e @two

™h—nnelsAD ™orresponding to four ™l—ssesX thum˜ (nger )exionD pointer (nger )exionD

middle (nger )exion —nd h—nd ™lose movements —re presented in (gure TFPQF „he

p—r—meters of e—™h ellipse will ˜e used to gener—te the initi—l inputEsets of F T M C

™l—ssi(erEmodelD for this t—sk the gener—lised ˜ell mem˜ership fun™tion @gbellmf A is

™hosenF F T M C E˜—sed input fuzzy sets initi—lis—tion for tr—in d—t— gives us the folE

lowing p—rtition of the input sp—™eD (gure TFPRF ‰ou h—ve o˜viously o˜served in this
        IST                        TFH   €erform—n™es of proposed p„wg —lgorithm




          pigure TFPPX „r—in —nd test s—mples distri˜ution of fe—ture M 2F



(gure the existen™eD in inputEPD of redund—nt sets @simil—r fuzzy setsAF these redunE

d—nt fuzzy sets ™—n ˜e removed using — simil—rity me—sure ‘TI“F „his initi—l model

with four rulesD whi™h des™ri˜es four ™l—sses with singleton ™onsequentsD h—s —ver—ge

™l—ssi(™—tion —™™ur—™y of UWFRIIV% giving 4IR4 mis™l—ssi(™—tions on the test d—t—D

(gure TFPSF st is possi˜le to lo™—te the mis™l—ssi(ed s—mples for e—™h ™l—ssF por the

(rst ™l—ssD thum˜ (nger )exionD there —re 4S4 mis™l—ssi(ed s—mplesD or UHFSVVP% ™orE

re™tD whi™h —re ™l—ssi(ed —s pointer (nger movementF e˜out the se™ond ™l—ssD pointer

(nger )exionD there —re —lso 4Q4 mis™l—ssi(ed s—mplesD or VPFQSPW% ™orre™tD whi™h

—re ™l—ssi(ed —s middle (nger movementF „he third ™l—ssD middle (nger )exionD h—s

only 4R4 mis™l—ssi(ed s—mple or UTFRUHT% ™orre™tD whi™h is ™l—ssi(ed —s pointer (nger

movementF the l—st ™l—ssD h—nd ™losingD h—s 4P4 mis™l—ssi(ed s—mplesD or VVFPQSQ%

™orre™tD whi™h —re ™l—ssi(ed —s middle (nger movementF
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                          ISU




pigure TFPQX illipses derived from           pigure TFPRX snput fuzzy sets initi—liE
T M C —lgorithm for tr—inEs—mplesF           s—tion using FTMC ™l—ssi(erEmodelF




pigure TFPSX wis™l—ssi(ed s—mples of initi—l fuzzy F T M C ™l—ssi(erEmodel for test
d—t—
        ISV                         TFH   €erform—n™es of proposed p„wg —lgorithm



b) Optimised FTMC classier-model

yptimis—tion pro™edure is —pplied in two stepsF „he (rst step ™on™erns nonline—r

p—r—meters using the gr—dientD see se™tion TFRFQF˜F „he se™ond step ™on™erns the opE

timis—tion of line—r p—r—meters @™onsequent p—r—metersA with line—r ve—st ƒqu—res

istim—tor @LSE AD see se™tion TFRFQF—F sniti—l F T M C ™l—ssi(™—tion —lgorithmD deE

s™ri˜ed —˜ove h—s found — good st—rting point in proximity of the glo˜—l minimumF

„his initi—l ™l—ssi(erEmodel h—d — ™l—ssi(™—tion —™™ur—™y equ—l to UWFRIIV%F ren™e

the f—rther —ppli™—tion of — few optimis—tion epo™hs will not h—ve — ˜ig e'e™t on overE

l—p of the mem˜ership fun™tions —nd will not ˜e timeE™onsumingF „he optimis—tionD

during only four epo™hsD of the initi—l F T M C E™l—ssi(er modelD (gure TFPRD on ˜oth

—nte™edents —nd ™onsequents p—r—meters using GD —nd LSE respe™tivelyD gives — new

rep—rtition of input sp—™eF „his rep—rtition is presented in (gure TFPTF    ‡e o˜t—in




     pigure TFPTX xew gebellmf fun™tions —fter R epo™hs F T M C optimis—tion


™onsequently the new ™l—ssi(™—tion —™™ur—™y equ—l to VTFUTRU% giving W s—mples of

mis™l—ssi(™—tionF „hey were 4IH4 mis™l—ssi(ed s—mples ˜efore optimis—tionD on the
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                             ISW




pigure TFPUX wis™l—ssi(ed s—mples of optimised F T M C ™l—ssi(erEmodel during R
epo™hs




d—t— testD (gure TFPUF ell these results —re resumed in the following (gure TFPVF efter

optimis—tion of these four initi—l Gebellmf fun™tionsD the following results —re o˜E

t—inedX

por the (rst ™l—ssD thum˜ (nger )exionD there is 4I4 mis™l—ssi(ed s—mple or WRFIIUT%

™orre™tD whi™h is ™l—ssi(ed —s pointer (nger movementF e˜out the se™ond ™l—ssD pointer

(nger )exionD there is 4I4 mis™l—ssi(ed s—mpleD whi™h is ™l—ssi(ed —s thum˜ moveE

mentD —nd 4P4 s—mples —s middle (nger )exion DVPFQSPW% ™orre™tF „he third ™l—ssD

middle (nger )exionD h—s 4Q4 mis™l—ssi(ed s—mples or VPFQSPW % ™orre™tD two of them

—re ™l—ssi(ed —s pointer (nger movementD —nd one —s rgF „he l—st ™l—ss Dh—nd ™losE

ingD h—s 4P4 mis™l—ssi(ed s—mples or VVFPQSQ% ™orre™tD whi™h —re ™l—ssi(ed —s middle

(nger movementF „he ™orresponding rules to the fuzzy sets of optimised F T M C
        ITH                          TFH   €erform—n™es of proposed p„wg —lgorithm




pigure TFPVX F T M C ™l—ssi(erEmodelX gorre™tE —nd misE™l—ssi(ed s—mples for e—™h
™l—ss —nd the interferen™es ˜etween them

™l—ssi(erEmodel —nd   their singleton output ™onsequents —re given in equ—tion TFSFIF
              
               1
              
                     if x is A1 —nd y is B1 then Zk = 0.4436 < 1, 5
              
                      if x is A2 —nd y is B2 then 1, 5 ≤ Zk = 1.522 < 2, 5
              
               2
     Classk =                                                                   @TFSFIA
               3
              
                     if x is A3 —nd y is B3 then 2, 5 ≤ Zk = 3.267 < 3, 5
              
                      if x is A4 —nd y is B4 then Zk = 4.072 ≥ 3, 5
              
               4



6.5.2 Multi layer perceptron classier-model
„his network is used in m—ny di'erent types of —ppli™—tionsD its —r™hite™ture h—s —

l—rge ™l—ss of network types with m—ny di'erent topologies —nd tr—ining methodsD

see se™tion TFPF „he num˜er of neurons in hidden l—yer is determined ˜—sed on their

perform—n™e in tr—ining pro™essF por oneEneuron outputEl—yerD log sigmoid tr—nsfer

fun™tion logsig is usedD whi™h gives —n output in the r—nge of H to IF „he output

r—nge ˜etween H —nd I will ˜e divided in four r—ngesD sin™e there —re four ™l—sses to

˜e identi(edD see „—˜le TFRF „he M LP xetwork is tr—inedD during IHH epo™hsD with
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                                      ITI




„—˜le TFRX yneEneuron outputEl—yer de(ned with log sigmoid tr—nsfer fun™tion
@logsig AD th—t is divided in four r—nges ˜etween H —nd I
             ™l—sses „—rget yutput yutput r—nge „ype of wovement
            gl—ssI        HFIPS           HFHH   E   HFPS         „hum˜ (nger
            gl—ssP        HFQUS           HFPS   E   HFSH         €ointer (nger
            gl—ssQ        HFTPS           HFSH   E   HFUS         middle (nger
            gl—ssR        HFVUS           HFUS   E   IFHH         r—nd ™losing



„—˜le TFSX M LP Emodel ™l—ssi(™—tion —™™ur—™y @™l—ssE —nd —ver—geE—™™ur—™yAD for difE
ferent hidden l—yer neuron num˜ersF @M2 timeEfrequen™y fe—tureA
                            gl—ssi(™—tion —™™ur—™y @test d—t—A %
              num˜er of     „hum˜      €ointer       widdle      rg      —ver—ge
               neurons
                  IH        WRFII      UHFSV         VVFPQ       WRFII    VTFUT
                  PH        WRFII      SVFVP         WRFII       VVFPQ    VQFVP
                  SH        WRFII      UHFSV         VPFQS       WRFII    VSFPW
                            xum˜er of ™orre™t ™l—ssi(ed inst—n™es GIU
                num˜er of    „hum˜       €ointer      widdle       rg    „ot—l
                 neurons
                     IH           IT       IP               IS     IT    SWGTV
                     PH           IT       IH               IT     IS    SUGTV
                     SH           IT       IP               IR     IT    SVGTV



di'erent num˜er of neurons in hidden l—yerX IHD PH —nd SH neuronsF „he o˜t—ined

™l—ssi(™—tion —™™ur—™y results —re presented in t—˜le TFSD in whi™h the in™re—sing of

neuronsEnum˜er in hidden l—yer doesn9t enh—n™e —lw—ys the —™™ur—™yF wore det—iled

resultsD (gure TFPWD —re given for the ˜est o˜t—ined M LP ™l—ssi(erEmodelD whi™h h—s

IH neuronsF sn the (rst ™l—ssD thum˜ (nger )exionD there is 4I4 mis™l—ssi(ed s—mpleD

or WRFII% ™orre™tD whi™h is ™l—ssi(ed —s pointer (nger movementF e˜out the se™ond

™l—ssD pointer (nger )exionD there —re 4P4 mis™l—ssi(ed s—mpleD whi™h —re ™l—ssi(ed —s
        ITP                        TFH   €erform—n™es of proposed p„wg —lgorithm




pigure TFPWX wis™l—ssi(ed s—mples of optimised M LP ™l—ssi(erEmodel during IHH
epo™hs

thum˜ movementD —nd 4P4 s—mples —s middle (nger )exion —nd 4I4 s—mple —s 4rg4

@UHFSV% ™orre™tAF „he third ™l—ssD middle (nger )exionD h—s 4P4 mis™l—ssi(ed s—mplesD

or VVFPQ % ™orre™tD whi™h —re ™l—ssi(ed —s 4rg4 movementF „he l—st ™l—ssD h—nd

™losingD h—s only 4I4 mis™l—ssi(ed s—mpleD or VVFPQSQ% ™orre™tD whi™h is ™l—ssi(ed —s

pointer (nger movementF
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                               ITQ



6.5.3 Radial Basis Networks classier-model

„he RBF xetwork is — one hidden l—yer neur—l xetwork with sever—l forms of r—di—l

˜—sis —™tiv—tion fun™tionsD like q—ussi—n fun™tionF „he output l—yer of this type of

network is line—rF q—ussi—n fun™tions —re monotone —nd their ™entre —nd r—dius —re

the p—r—meters of the RBF EmodelF

RBF networks h—ve ˜een —pplied for m—ny —ppli™—tions in™luding —pproxim—tion

‘PW“D modelling ‘TT“ —nd ™l—ssi(™—tion ‘PI“D more det—ils see ‘SS“ ‘II“F sn ™l—ssi(™—tion

™—se the outputs l—yer ™orrespond to — ™l—ssesF „his method exist in M AT LAB tool

—s 4newrb4 ™omm—nd for whi™h the tr—ining implement—tion is the orthogon—l le—st

squ—res @yvƒA le—rning —lgorithm ‘IQ“F „he method of ™re—ting neurons or ™entres

one —t — time @newr˜AD is usedF sn e—™h iter—tion the input ve™tor is —pplied to ™re—te

— new neuronD then the error of the new network is ™he™kedD if it is not low enough the

next neuron is —ddedF „his pro™edure is repe—ted until the error go—l is metD or the

m—ximum num˜er of neurons is re—™hedF ƒo is possi˜le to (nd the sm—llest network

th—t ™—n solve the pro˜lem within — given error go—lF „he r—te of ™l—ssi(™—tion is

depending on the hidden unit spre—d v—luesF hi'erent v—lues for spre—d p—r—meters

˜etween HFS —nd PFS —re given with — step of HFPF „he —im is to (nd the optim—l v—lue

of spre—dD whi™h is in this ™—se equ—l to HFS —nd HFU see (gure TFQHF

 yne of these two ˜est spre—d v—lues is ™hosenF „he RBF E™l—ssi(er model is ˜uilt —nd

tested using M 2 extr—™ted fe—tureF gl—ssi(™—tion results —re presented in (gure TFQIF

„he glo˜—l ™l—ssi(™—tion —™™ur—™y is equ—l to VQFVP % giving 4II4 mis™l—ssi(ed s—mE

plesF wore det—iled results for this ˜est o˜t—ined RBF ™l—ssi(erEmodelD with spre—d

v—lue equ—l to HFUD —re givenF sn the (rst ™l—ssD thum˜ (nger )exionD there is 4I4 misE

™l—ssi(ed s—mpleD or WRFII% ™orre™tD whi™h is ™l—ssi(ed —s pointerE(nger movementF
        ITR                        TFH   €erform—n™es of proposed p„wg —lgorithm




pigure TFQHX ever—ge —™™ur—™y —™™ording to di'erent spre—d v—lues of RBF networkF
@por M 2 timeEfrequen™y dom—in fe—tureA




              pigure TFQIX wis™l—ssi(ed s—mples of RBF E™l—ssi(erEmodel
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                           ITS



sn the se™ond ™l—ssD pointer (nger )exionD there —re 4P4 mis™l—ssi(ed s—mpleD whi™h

—re ™l—ssi(ed —s thum˜E(nger movementD —nd 4P4 s—mples —s middleE(nger )exion

@UTFRU% ™orre™tAF „he third ™l—ssD middleE(nger )exionD h—s 4P4 mis™l—ssi(ed s—mE

plesD or VVFPQ % ™orre™tD whi™h —re ™l—ssi(ed —s pointerE(nger movementF „he l—st

™l—ssD h—nd ™losingD h—s only 4R4 mis™l—ssi(ed s—mplesD or UTFRU% ™orre™tD whi™h —re

™l—ssi(ed —s middle (nger movementF ell these results —re resumed in the following

(gure TFQPF




pigure TFQPX RBF ™l—ssi(erEmodelX gorre™tE —nd misE™l—ssi(ed s—mples for e—™h ™l—ss
—nd the ™l—ssi(™—tionEinterferen™es ˜etween them




6.5.4 Learning Vector Quantization classier-model
ve—rning †e™tor u—ntiz—tion ‘QU“ ‘QV“ networks ™—n ™l—ssify —ny set of input ve™tors

like non line—rly sep—r—˜le sets of input ve™torsF sts —r™hite™ture resem˜les to th—t

of unsupervised ™ompetitive le—rning networkD ex™ept th—t e—™h output is —ssigned

to — t—rget ™l—ss —nd works in two stepsF sn (rst step it uses —n unsupervised d—t—

™lustering method to lo™—te sever—l ™lustersF sn se™ond step it optimises the ™luster
        ITT                         TFH   €erform—n™es of proposed p„wg —lgorithm



™entresF „he num˜er of ™lusters ™—n ˜e spe™i(ed a priori or determined vi— ™luster

te™hniquesF st is —˜le to redu™e l—rge d—t— sets to — sm—ller num˜er of ™ode˜ook

ve™tors @™luster ™entresA suit—˜le for d—t— ™ompressingF LV Q network used in this

work h—s four neurons in the (rst ™ompetitive l—yer —nd one neuron for e—™h ™l—ss in

the se™ond line—r l—yerF efter IS tr—ining epo™hsD the optim—l num˜er of neurons in

™ompetitive l—yer found is IP or IU neuronsD (gure TFQQF F „he v—lue of IP neurones




pigure TFQQX LV Q ™l—ssi(erEmodelX ever—ge —™™ur—™y —™™ording to ™ompetitive neuE
rones num˜er por M2 timeEfrequen™y dom—in fe—ture


is ™hosen to ˜uilt our LV Q ™l—ssi(erEmodelD then this model is optimised during IHH

epo™hsF „his optimis—tion le—ds to the following ™l—ssi(™—tion resultsD (gure TFQR F sn

the (rst ™l—ssD thum˜E(nger )exionD there is no mis™l—ssi(ed s—mplesD or IHH% ™orre™tF

sn the se™ond ™l—ssD pointerE(nger )exionD there —re 4S4 mis™l—ssi(ed s—mplesD whi™h

—re ™l—ssi(ed —s thum˜E(nger movementD —nd 4I4 s—mple —s middleE(nger movement

@TRFUH% ™orre™tAF „he third ™l—ssD middleE(nger )exionD h—s no mis™l—ssi(ed s—mples

@IHH % ™orre™tAF „he l—st ™l—ssD h—nd ™losingD h—s only 4P4 mis™l—ssi(ed s—mplesD or

VVFPQ% ™orre™tD whi™h —re ™l—ssi(ed —s middleE(nger movementF ell these results —re

resumed in the following (gure TFQSF
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                          ITU




pigure TFQRX wis™l—ssi(ed s—mplesD of optimised LV Q ™l—ssi(erEmodel during IHH
epo™hs




pigure TFQSX LVQ ™l—ssi(erEmodelX gorre™tE —nd misE™l—ssi(ed s—mples for e—™h ™l—ss
—nd the ™l—ssi(™—tionEinterferen™es ˜etween them
        ITV                         TFH   €erform—n™es of proposed p„wg —lgorithm



6.5.5 Classication accuracy comparison
sn this se™tion the previous four studied intelligent ™omput—tion—l ™l—ssi(™—tion methE

odsD M LP, RBF —nd LV QD with the proposed supervised F T M C ™l—ssi(™—tion —lE

gorithm will ˜e ™omp—redF sn this ™—se the extr—™ted M 2 timeEfrequen™y fe—ture is

usedF „op (gure shows the methods results ™omp—rison for e—™h ™l—ss of h—nd moveE

ment ™l—ssi(™—tionF fottom (gure shows methods perform—n™e ™omp—rison for glo˜—l

™l—ssi(™—tionF pollowing (gure TFQT resumes —ll previous resultsF st9s import—nt to reE

mem˜er th—t this proposed —ppro—™h h—s needed only R tr—ining epo™hs in ™omp—rison

with IHH tr—ining epo™hs for other methodsF




pigure TFQTX gl—ssi(™—tion —™™ur—™y ™omp—rison of M LP D RBF D LV Q —nd proposed
F T M C —lgorithm with extr—™ted M 2 timeEfrequen™y fe—tureF




6.5.6 Conclusion
sn ™—se of dyn—mi™—l ™omplex systemsD like fore—rm iwq sign—ls re™ognitionD intelliE

gent ™omput—tion—l methods show their e0™ien™y to de—l with su™h ™omplex systems
TFSF gomp—rison ˜tween MLP, RBF, LVQ and FTMC                              ITW



—nd give good ™l—ssi(™—tionEmodelsF

„he str—tegy to ™hoose ˜etween di'erent ™l—ssi(™—tion methods is of gre—t imporE

t—n™eF sn ™—se of onEline prosthesis ™ontrol or exoskeleton devi™es ™ontrolD the needed

time for sign—l —™quisitionD then for pro™essing till de™ision ™ontrol should ˜e shortF

„herefor the ™hoi™e de™ision of this method to use for ™l—ssi(™—tion should ™onsiders

˜oth time ™onsuming —nd perform—n™eF por these ™onsider—tions this fuzzy F T M C

™l—ssi(erE—lgorithm is proposed for su™h —ppli™—tion like surf—™e iwq sign—ls ™l—ssi(E

™—tionF es it is proved in this se™tion TFSD this —lgorithm presents —™™ept—˜le resultsF

sts —dv—nt—ge ™—n ˜e seen in optimis—tion methodsD whi™h —re simple —nd not time

™onsumingD like qr—dient hes™ent @GDA —nd ve—st ƒqu—red irror @LSE AD —nd —lso

utilis—tion of simple „rimmed we—n method for determin—tion of initi—l input fuzzy

sets @initi—l ™l—ssi(erEmodel stru™tureAF
IUH   TFH   €erform—n™es of proposed p„wg —lgorithm
Chapter 7
Inuence evaluation of important
parameters

7.1 Introduction
efter ™ompleting the ƒtudy of iwq sign—l pro™essing ph—ses —nd ™l—ssi(™—tion proE

™eduresD this (rst p—rt of thesis will ˜e (n—lised ˜y some di'erent re—l —ppli™—tion

studiesF „his ™h—pter will ™onsider the in)uen™e or the e'e™t of import—nt p—r—meE

ters on ™l—ssi(™—tion —™™ur—™yF „he me—surement of surf—™e iwq sign—ls is depending

on di'erent f—™torsF ren™e the re™ognition of these sign—ls ™orresponding to their musE

™le dyn—mi™s h—s to t—ke in ™onsider—tion the following f—™torsD whi™h will ˜e studied

in det—ilsX




a) Eect of lter frequency band: di'erent (lter frequen™y ˜—nds will ˜e —pplied
      to test their e'e™t on ™l—ssi(™—tion perform—n™esF


b) Eect of noise threshold level: di'erent noise threshold levels ˜—sed on noise9s
      st—nd—rd devi—tion will ˜e tested —nd ™omp—red

                                         IUI
        IUP                        UFH    sn)uen™e ev—lu—tion of import—nt p—r—meters



c) Eect of EMG signal length and sampling frequency: di'erent s—mpling freE
     quen™ies will ˜e tested —lso in ™om˜in—tion with di'erent iwq sign—l lengthsF


por —n —v—il—˜le ™on™lusionsD di'erent ™l—ssi(™—tion methods —re ™onsideredD three

methodsD —nd —lso seven di'erent fe—tures —re usedF „—king in ™onsider—tion the reE

sults studied in se™tion RFRF „hese fe—tures —re those extr—™ted from iwq sign—ls

timeEfrequen™y —n—lysisX

E zero order moment @M0 AF

E (rst order moment @M1 AF

E se™ond order moment @M2 AF

E gentr—l frequen™y @Fcnt AF

E prequen™y v—ri—n™e @Fvar AF

E prequen™y st—nd—rd devi—tion @Fstd AF

E inergy of sign—l @Eng AF

hi'erent intelligent ™omput—tion—l ™l—ssi(™—tion methods —re tested to get —lso more

—v—il—˜le resultsF „hese methodsD des™ri˜ed in ™h—pter T —reX ‚—di—l f—sis pun™tion

xetworks @RBF AD puzzy ƒu˜tr—™tive glustering @F SC A —nd proposed fuzzy trimmed

me—n ™l—ssi(erE—lgorithm @F T M C AF

„he re—son th—t in™ited us to use these di'erent ™l—ssi(™—tion methods is to ™on(rm

if the in)uen™e of e—™h p—r—meter is depending on ™l—ssi(™—tionEmethod or notF sf

the in)uen™e of — p—r—meter ™h—nges ˜etween these methodsD then it9s not possi˜le

to get — ™on™lusion —˜out the in)uen™e of this p—r—meterF ytherwise if this in)uen™e

of — p—r—meter is the s—me for —ll ™l—ssi(™—tion methodsD in this ™—se it9s possi˜le for

us to ™on™lude whi™h type of in)uen™e h—s this p—r—meterF        fefore the ˜eginning

of m—them—ti™—l studyD it is prefer—˜leD —s we ˜elieveD to show —nd to expl—in these
UFIF sntrodu™tion                                                       IUQ




    pigure UFIX Butterworth-D chebyshev-1 E —nd Elliptic E(lter frequen™y ˜—ndsF




            pigure UFPX xoise threshold level —nd iwq sign—l lengthF
        IUR                        UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



p—r—meter e'e™ts using only s™hem—ti™ pro™edureF pigure UFI presents three (lter freE

quen™y ˜—nds using ˜utterworthD chebyshev-1 —nd Elliptic (ltersF „he two following

p—r—metersX noise threshold level —nd iwq sign—l lengthD —re presented in (gure UFP



7.2 Frequency Bandpass eect
„he study of sign—l (ltering to remove undesired sign—lsD whi™h ™ontri˜ute to drown

the import—nt inform—tion in the sign—lD is des™ri˜ed in se™tion RFQFTF „he ™hoi™e of

the (lter type —nd its order is ˜—sed on the study did —lso in se™tion RFQFTF „he re™ogE

nition of this sign—l is depending on its inform—tion ™ontentsD if this inform—tion is

kipped inside the sign—l —fter (lteringD then the sign—l re™ognition —™™ur—™y in™re—sesD

otherwise it will ˜e worseF „he o˜je™tive of this se™tion is to show the e'e™t of (lterE

ing —nd to get the tools of the ˜est (ltering str—tegyF sn the liter—tureD it is known

th—t the (lter frequen™y ˜—nd to elimin—te undesir—˜le noise frequen™ies is given in

the r—nge of 20Hz —nd 500HzF „hrough the study of this se™tionD we will h—ve the

possi˜ility to ™on™lude if this p—ssE˜—nd frequen™y is —lw—ys usefulF

„hree di'erent frequen™y p—ssE˜—ndsD 10-300HzD 10-500Hz —nd 10-800HzD —re sele™ted

to ˜e tested for —ll our seven fe—tures des™ri˜ed —˜oveF „hese seven di'erent fe—tures

—re divided —lso in three di'erent groups —™™ording to their ™ommon ˜eh—viours reE

g—rding these frequen™yE˜—ndsF „he (rst group is ™omposed of the three (rst fe—turesX

M0, M1 and M2F „he se™ond group is ™omposed of the next three fe—turesX Fcnt,

Fvar and FstdF „he l—st group is presented with only one fe—tureX EngF „he perforE

m—n™es of e—™h group —re ™—l™ul—ted for —ll the three frequen™yE˜—nds de(ned —˜oveF

sn this w—y it will ˜e possi˜le to look for the frequen™yE˜—nd for e—™h fe—ture groupD

whi™h gives the ˜est ™l—ssi(™—tion perform—n™eF
UFPF prequen™y f—ndp—ss e'e™t                                           IUS



7.2.1 Classication performance with RBF -based approach

…sing RBF ™l—ssi(™—tion methodD (gure UFQD it ™—n ˜e seen th—t the (rst fe—ture group

@M0, M1 and M2 A h—s good glo˜—l ™l—ssi(™—tion perform—n™e in the frequen™yE˜—nd

of 10-300HzF por the se™ond fe—tures group @Fcnt, Fvar and Fstd A the frequen™yE˜—nd

of 10-800Hz gives the ˜est glo˜—l ™l—ssi(™—tion perform—n™eF „he glo˜—l ™l—ssi(™—tion

perform—n™e of third fe—ture groupD ingD seems unsensi˜le to the frequen™yE˜—ndD it

gives —lmost the s—me perform—n™es for these three frequen™y ˜—ndsF „hese results

—re o˜t—ined in the ™—se of four di'erent spre—d v—lues ˜etween HFR —nd IFT with —

step of HFR for these seven fe—turesF




pigure UFQX pilter frequen™y €—ssE˜—nd e'e™t on ™l—ssi(™—tion perform—n™e using RBF
™l—ssi(™—tion method for )exion movements of three (ngersX „hum˜D pointer —nd
middleF
        IUT                       UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



7.2.2 Classication performance with FSC -based approach

vike with RBF methodD FSC ™l—ssi(™—tion methodD (gure UFRD h—s —lmost the s—me

resultsF „he (rst groupEfe—ture @M0, M1 and M2 A h—s ˜est ™l—ssi(™—tion perforE

m—n™e in the frequen™yE˜—nd of 10-300HzF „he ˜est ™l—ssi(™—tion perform—n™e for

the se™ond groupEfe—ture @Fcnt, Fvar and Fstd A is given ˜y frequen™yE˜—nd of 10-

800HzF „he ™l—ssi(™—tion perform—n™e of third fe—ture groupD EngD seems unsensi˜le

to the frequen™yE˜—ndD it gives —lmost the s—me perform—n™es for these three freE

quen™y ˜—ndsF „hese results —re o˜t—ined in the ™—se of four di'erent r—dius v—lues

˜etween HFP —nd HFV with — step of HFP for these seven fe—turesF




pigure UFRX pilter frequen™y €—ssE˜—nd e'e™t on ™l—ssi(™—tion perform—n™e using FSC
™l—ssi(™—tion method for )exion movements of three (ngersX „hum˜D pointer —nd
middleF
UFPF prequen™y f—ndp—ss e'e™t                                             IUU



7.2.3 Classication performance with FTMC algorithm
€roposed —lgorithm FTMC givesD vike with RBF —nd FSC methodsD the s—me reE

sults of ™l—ssi(™—tion perform—n™esD whi™h —re shown in (gure UFSF por the (rst fe—ture

group @M0, M1 and M2 A the ˜est ™l—ssi(™—tion perform—n™e h—s ˜een found in the

frequen™yE˜—nd of 10-300HzF „he ˜est ™l—ssi(™—tion perform—n™e for the se™ond fe—E

ture group @Fcnt, Fvar and Fstd A is given ˜y frequen™yE˜—nd of 10-800HzF „he ™l—sE

si(™—tion perform—n™e of third fe—ture groupD EngD seems unsensi˜le to the frequen™yE

˜—ndD it gives —lmost the s—me perform—n™es for these three frequen™y ˜—ndsF „hese

results —re o˜t—ined in the ™—se of four di'erent trimming per™ent—geD β D v—lues ˜eE

tween HFTR —nd HFWR with — step of HFI for these seven fe—turesF




pigure UFSX pilter frequen™y €—ssE˜—nd e'e™t on ™l—ssi(™—tion perform—n™e using proE
posed FTMC ™l—ssi(™—tion —lgorithm for )exion movements of three (ngersX „hum˜D
pointer —nd middleF
         IUV                        UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



7.2.4 Conclusion
st is possi˜le for us to ™on™lude nowD —fter these —lmost s—me results found with these

three di'erent ™l—ssi(™—tion methods —nd seven di'erent fe—turesD th—t the optim—l

frequen™y ˜—nd is depending on the n—ture of the fe—tureF „he study in this se™tion

using three di'erent ™l—ssi(™—tion methods —nd seven fe—tures gives the optim—l freE

quen™y ˜—nd 10-300Hz for the (rst group @M0, M1 and M2 AF por the se™ond group

Fcnt, Fvar and FstdD optim—l frequen™y ˜—nd is 10-800HzF pin—lly for the third fe—E

ture groupD EngD ™l—ssi(™—tion —™™ur—™y it9s —lmost the s—me for —ll three frequen™y

˜—ndsF



7.3 Threshold level eect
‡h—t is the e'e™t of the noise9s threshold level on the perform—n™e of iwq sign—l

™l—ssi(™—tion @re™ognitionAcF „his question h—d gener—ted intensive dis™ussion ˜eE

tween rese—r™hersF „his p—r—meter is very import—nt ˜e™—use it represents the (rst

step of iwq sign—l pro™essingD see se™tion RFPF „he ˜eginning time of iwq sign—l

—™tiv—tion is depending on this referen™e levelD therefor this p—r—meter is ™onsidered

—s very sensi˜le f—™torF sn this se™tion three di'erent v—lues of this p—r—meter —re

testedD whi™h —re rel—tive to the v—lue of noise9s st—nd—rdEdevi—tion @Std AF sf the

noise9s st—nd—rdEdevi—tion v—lue is given —s T hresholdstd D then these v—lues —re given

—sX HFST hresholdstd D T hresholdstd —nd PT hresholdstd F

yur seven di'erent fe—tures —re divided in three di'erent groups —™™ording to their

™ommon ˜eh—viours reg—rding these v—luesD see se™tion —˜oveF „he ™hoi™e of v—lue

of frequen™yE˜—nds for e—™h fe—ture group is de(ned using the optim—l result found

in the pre™eding se™tion UFQF „hese frequen™yE˜—nds —reX 10-300Hz for fe—ture group
UFQF „hreshold level e'e™t                                                 IUW



@M0, M1 and M2 AD 10-800Hz for fe—ture group @Fcnt, Fvar and Fstd AD —nd 10-500Hz

for fe—ture EngF



7.3.1 Classication performance with RBF -based approach
…sing RBF ™l—ssi(™—tion methodD (gure UFTD it ™—n ˜e seenD th—t for the (rst fe—tures

group @M0, M1 and M2 A (ltered in frequen™y ˜—nd of 10-300Hz h—s good ™l—ssi(™—tion

perform—n™e for the noise9s threshold level equ—l to 2 · T hresholdstd F „he se™ond




pigure UFTX xoise threshold level e'e™t on ™l—ssi(™—tion perform—n™e using RBF ™l—sE
si(™—tion method for )exion movements of three (ngersX „hum˜D pointer —nd middleF


fe—ture group @Fcnt, Fvar and Fstd A (ltered in frequen™y ˜—nd of 10-800 Hz h—s

good ™l—ssi(™—tion perform—n™e with noise9s threshold level equ—l to 1 · T hresholdstd F

pin—lly the ™l—ssi(™—tion perform—n™e of third fe—ture groupD EngD (ltered in frequen™y

˜—nd of 10-500Hz get good ™l—ssi(™—tion perform—n™e for the noise9s threshold level

equ—l to 2 · T hresholdstd AF „hese results —re o˜t—ined in the ™—se of four di'erent
        IVH                        UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



spre—d v—lues of RBF mem˜ership fun™tions ˜etween HFR —nd IFT with — step of HFRF


7.3.2 Classication performance with FSC -based approach
„his method gives the s—me resultsD see (gure UFUD —s with RBF method des™ri˜ed

—˜ove in se™tion UFQFIF por the (rst group @M0, M1 and M2 A (ltered in frequen™y ˜—nd




pigure UFUX xoise threshold level e'e™t on ™l—ssi(™—tion perform—n™e using FSC ™l—sE
si(™—tion method for )exion movements of three (ngersX „hum˜D pointer —nd middleF


of 10-300HzD the ™l—ssi(™—tion is glo˜—lly performed for the threshold level equ—l to

2·T hresholdstd F „he se™ond fe—tures groupX Fcnt, Fvar and FstdD (ltered in frequen™y

˜—nd of 10-800Hz h—s good ™l—ssi(™—tion perform—n™e for the threshold level equ—l

to 1 · T hresholdstd F pin—lly the ™l—ssi(™—tion perform—n™e of the third fe—ture groupD

EngD (ltered in frequen™y ˜—nd of 10-500Hz get good ™l—ssi(™—tion perform—n™e for

the threshold level equ—l to 2 · T hresholdstd F „hese results —re o˜t—ined in the ™—se

of four di'erent r—dius v—lues of FSC ™lusters ˜etween HFP —nd HFV with — step of HFPF
UFQF „hreshold level e'e™t                                               IVI



7.3.3 Classication performance with FTMC algorithm
‡ith this proposed ™l—ssi(™—tion model the resultsD (gure UFVD —re the s—me with those

des™ri˜ed —˜ove using RBF —nd FSC methodsF „hese results —re o˜t—ined in the ™—se




pigure UFVX xoise threshold level e'e™t on ™l—ssi(™—tion perform—n™e using proposed
FTMC ™l—ssi(™—tion method for )exion movements of three (ngersX „hum˜D pointer
—nd middleF


of four di'erent trimming per™ent—geD β D v—lues of FTMC ellipses ˜etween HFTR —nd

HFWR with — step of HFIF



7.3.4 Conclusion
xoise threshold level p—r—meter is — de™isive f—™tor for iwq sign—ls ™l—ssi(™—tionF

st is di0™ult to give —n optim—l v—lueF „here —re some developed methodsD in the

liter—tureD whi™h tried to optimise this p—r—meterF „he study of this se™tion using

three di'erent ™l—ssi(™—tion methods —nd seven fe—tures led to the v—lue of noise9s
        IVP                        UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



threshold level equ—l to PT hresholdstd for the (rst group @M0, M1 and M2 A —nd the

third fe—ture groupD EngF por the se™ond group Fcnt, Fvar and FstdD ˜oth noise

threshold v—lues 1 · T hresholdstd —nd 2 · T hresholdstd —re optim—lF



7.4 Both signal length and sampling frequency ef-
    fects
„his studyD whi™h ™onsiders the e'e™t of ˜oth iwq sign—l length —nd s—mpling freE

quen™y p—r—meters on neuromus™ul—r sign—ls re™ognitionD is of — gre—t import—n™eF st

helps to optimise the ™hoi™e of these p—r—meter v—lues for the ˜est perform—n™es —nd

in the s—me time for the shorter online pro™essingEtimeF

„he ™onsidered iwq sign—l length h—s — signi(™—nt import—n™e for the ™l—ssi(™—tion

perform—n™e for the —ll iwq sign—lF sf this length is of sm—ll dur—tionD it will ˜e

possi˜le for us to t—lk —˜out iwq sign—l predi™tionF sn this ™—se the t—sk ˜e™omes

predi™tion —nd ™l—ssi(™—tionF „he ™l—ss of this —ll iwq —™tiv—tion sign—l is predi™ted

only from the ˜eginning sign—l p—rtF „hree di'erent v—luesD SIP s—mples @128ms AD

IHPR s—mples @256ms A —nd ISQT s—mples @384 ms A —re ™onsideredF st is known th—t

if the ™onsidered sign—l length p—rt is ˜iggerD then the ™l—ssi(™—tion perform—n™e is

˜etterD ˜ut the rese—r™hers in this dom—in —re limited this length ˜e™—use of onlineE

pro™essing ™onsider—tionF ‡e ™—n s—yD ˜—sed on our study in this se™tionD th—t this

monotone positive in)uen™e of sign—l length is not —lw—ys veri(ed if we t—ke —dditionE

—lly in ™onsider—tion the s—mpling frequen™y p—r—meterF „hree di'erent ƒ—mpling

frequen™y p—r—meters —re usedD whi™h —reX 1kHz, 2kHz and 4kHzF „wo fe—ture groups

—re ™onsidered —lsoD whi™h —reX M0, M1 and M2D (ltered with frequen™y ˜—nd of 10-

300HzD —nd Eng (ltered with frequen™y ˜—nd of 10-500HzF „he v—lue of noise ˜—selineD
UFRF foth sign—l length —nd s—mpling frequen™y e'e™ts                      IVQ



see —˜ove study in se™tion UFQD is ™onsidered equ—l to two times noise9s threshold v—lue

@PT hresholdstd AF „hree ™l—ssi(™—tion methods —re —pplied for e—™h fe—ture groupD —nd

the results —re regrouped together in one (gure for e—™h methodF


7.4.1 Classication performance with RBF -based approach
a) Case of feature-group M0, M1 and M2

…sing RBF ™l—ssi(™—tion method it ™—n ˜e seen in (gure UFWD for the (rst fe—tureEgroup

@M0, M1 and M2 A (ltered in frequen™y ˜—nd 10-300Hz with noise ˜—seline equ—l to

2 T hresholdstd D th—t the ™l—ssi(™—tion perform—n™e does not in™re—se proportion—lly

with the in™re—sing in sign—l lengthF sf the (rst frequen™y s—mpling v—lue 1kHz is




pigure UFWX ƒ—mpling frequen™y —nd sign—l length e'e™t on ™l—ssi(™—tion perform—n™e
in ™—se of M0, M1 and M2 fe—tures using RBF ™l—ssi(™—tion methodF


™onsideredD the ™l—ssi(™—tion perform—n™e de™re—ses when the sign—l length in™re—ses

from the (rst length SIP s—mples @128ms A to the se™ond length IHPR s—mples @256ms AD
        IVR                        UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



—nd then this perform—n™e in™re—ses for the third v—lue of PHRV s—mples @512ms AF sn

this ™—seD for 1kHz s—mpling frequen™yD the optim—l —nd the pr—™ti™—l v—lue for onlineE

pro™essing is the v—lue of SIP s—mples @128ms AF „hese two p—r—metersD 1kHz s—mpling

frequen™y —nd 128ms sign—l lengthD give —lmost the s—me perform—n™e if we ™onsider

the v—lues of ISQT s—mples @384ms A for sign—l length —nd 1kHz for s—mpling frequen™yD

whi™h require four times more of pro™essingEtimeF

por the se™ond —nd third frequen™y s—mpling v—luesD 2kHz —nd 4kHz (gure UFWD the

™l—ssi(™—tion perform—n™e is proportion—lly in™re—sing with the sign—l lengthF fut for

˜oth ™—sesD 2kHz —nd 4kHz frequen™y s—mpling v—luesD the ™l—ssi(™—tion perform—n™es

—re —lmost the s—me for sign—l length of IHPR s—mples @256ms A —nd ISQT s—mples

@384ms AF prom these results it9s possi˜le now to ™hoose the optim—l v—lues of these

two p—r—metersD whi™h —reX 256ms for sign—l length —nd 2kHz for s—mpling frequen™yF

„hese v—lues s—tisfy ˜oth good ™l—ssi(™—tion perform—n™e —nd redu™ed pro™essingE

timeF „he ™l—ssi(™—tion perform—n™e is equ—l to WS%D with fe—ture M0D in ™—se of

RBF spre—d v—lue equ—l to IFTF


b) Case of Eng feature

por the se™ond fe—tureEgroupD EngD (ltered in frequen™y ˜—nd of 10-500HzD —nd with

noise ˜—seline equ—l to 2 T hresholdstd D the ™l—ssi(™—tion perform—n™e does not inE

™re—se proportion—lly with the in™re—sing in sign—l lengthF prom the results shown in

(gure UFIHD it9s possi˜le to ™hoose the optim—l v—lues of these two p—r—metersX 128ms

for sign—l length —nd 2kHz for s—mpling frequen™yD whi™h s—tisfy ˜oth good ™l—ssi(™—E

tion perform—n™e —nd redu™ed pro™essingEtimeD rel—tively to —ll other v—lues of these

two p—r—metersF „he ™l—ssi(™—tion perform—n™e is equ—l UW% m—xF
UFRF foth sign—l length —nd s—mpling frequen™y e'e™ts                   IVS




pigure UFIHX ƒ—mpling frequen™y —nd sign—l length e'e™t on ™l—ssi(™—tion perform—n™e
in ™—se of Eng fe—tureD using RBF ™l—ssi(™—tion methodF


7.4.2 Classication performance with FSC -based approach


a) Case of feature-group M0, M1 and M2


prom the results shown in (gure UFIID —nd using the s—me pro™edureD see —˜ove study

se™tion UFRFIF—D it9s possi˜le to ™hoose the optim—l v—lues of these two p—r—metersD

whi™h —reX 256ms for sign—l length —nd 2kHz for s—mpling frequen™yF „hese v—lues

s—tisfy ˜oth good ™l—ssi(™—tion perform—n™es —nd redu™ed pro™essingEtimeF „he ™l—sE

si(™—tion perform—n™e is equ—l to WU% m—xD with fe—ture M0D in ™—se of FSC r—dius

v—lue equ—l to HFVD —nd redu™ed pro™essingEtimeF
        IVT                       UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters




pigure UFIIX ƒ—mpling frequen™y —nd sign—l length e'e™t on ™l—ssi(™—tion perform—n™e
in ™—se of frequen™y moment fe—tures using FSC ™l—ssi(™—tion methodF

b) Case of Eng feature

elso from the results shown in (gure UFIPD —nd using the s—me pro™edureD see —˜ove

study se™tion UFRFIF˜D it9s possi˜le to ™hoose the optim—l v—lues of these two p—r—mE

etersD whi™h —reX 128ms for sign—l length —nd 2kHz for s—mpling frequen™yF „hese

v—lues s—tisfy ˜oth good ™l—ssi(™—tion perform—n™esD whi™h is equ—l to VH% m—xD in

™—se of FSC r—dius v—lue equ—l to HFTD —nd redu™ed pro™essingEtimeF
UFRF foth sign—l length —nd s—mpling frequen™y e'e™ts                   IVU




pigure UFIPX ƒ—mpling frequen™y —nd sign—l length e'e™t on ™l—ssi(™—tion perform—n™e
in ™—se of Eng fe—tureD using FSC ™l—ssi(™—tion methodF

7.4.3 Classication performance with FTMC algorithm
a) Case of feature-group M0, M1 and M2

prom the results shown in (gure UFIQD —nd using the s—me pro™edureD see —˜ove study

se™tion UFRFIF—D it9s possi˜le to ™hoose the optim—l v—lues of these two p—r—metersD

whi™h —reX 256ms for sign—l length —nd 2kHz for s—mpling frequen™yF „hese v—lues

s—tisfy ˜oth good ™l—ssi(™—tion perform—n™e —nd redu™ed pro™essingEtimeF „he ™l—sE

si(™—tion —™™ur—™y is equ—l to WS%D with fe—ture M1D in ™—se of trimming per™ent—geD

β D equ—l to HFVSD


b) Case of Eng feature

sn the s—me w—yD from the results shown in (gure UFIRD —nd using the s—me pro™edureD

see —˜ove study se™tion UFRFIF˜D it9s possi˜le to ™hoose the optim—l v—lues of these
        IVV                      UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters




pigure UFIQX ƒ—mpling frequen™y —nd sign—l length e'e™t on ™l—ssi(™—tion perform—n™e
in ™—se of frequen™y moment fe—tures using FTMC ™l—ssi(™—tion methodF

two p—r—metersD whi™h —reX 128ms for sign—l length —nd 2kHz for s—mpling frequen™yF

„hese v—lues s—tisfy ˜oth good ™l—ssi(™—tion perform—n™esD whi™h is equ—l to VP%

m—xD in ™—se of trimming per™ent—geD β equ—l to HFWRD —nd redu™ed pro™essingEtimeF
UFRF foth sign—l length —nd s—mpling frequen™y e'e™ts                     IVW




pigure UFIRX ƒ—mpling frequen™y —nd sign—l length e'e™t on ™l—ssi(™—tion perform—n™e
in ™—se of Eng fe—tureD using FTMC ™l—ssi(™—tion methodF


7.4.4 Conclusion

„he ™hoi™e of iwq sign—l length —nd ƒ—mpling frequen™y v—lues —re of — gre—t imporE

t—n™e for the optimis—tion of pro™essingEtime ™onsumm—tion —nd for the ™l—ssi(™—tion

perform—n™esF es it h—s ˜een shown in this studyD it9s possi˜le with only — p—rt of

—™tiv—tion iwq sign—l length to predi™t —nd re™ognise the —ll —™tiv—tion sign—lF woreE

overD for some fe—turesD — shorter p—rt of —™tiv—tion iwq sign—l length ™—n predi™t

—nd ™l—ssify ˜etter th—n with longer oneF elso —˜out frequen™y s—mplingD sm—ller v—lE

ues ™—n give ˜etter resultsF fe™—use the n—ture of fe—tures present di'erent ˜eh—viors

we should not use the s—me v—lues of these p—r—meters for —ll fe—turesF
        IWH                      UFH   sn)uen™e ev—lu—tion of import—nt p—r—meters



7.5 Conclusion
„he o˜je™tive of this gh—pter w—s fo™used on the study of import—nt f—™tors th—t

in)uen™e the iwq sign—l represent—tionD the ™l—ssi(™—tion —™™ur—™y —nd pro™essing

time ™onsumingF por getting —˜le results three di'erent ™l—ssi(™—tion methods —nd

seven di'erent fe—tures —re usedF „hrough this study we ™ould show how these p—E

r—meters in)uen™e iwq sign—l re™ognitionF „he go—l w—s to ™l—rify whi™h p—r—meters

—re import—nt —nd how to pro™eed the ™hoi™e of the optim—l v—luesF
Chapter 8
Musculoskeletal dynamics
identication

8.1 Introduction

‡holeE˜ody movement is —™hieved with help of the inter—™tion ˜etween the neuromusE

™ul—r sign—l ™ontrol —nd mus™uloskelet—l dyn—mi™sF we—sured neuromus™ul—r sign—ls

—s iwq sign—ls —re investig—ted in the (rst p—rt of this thesisF st w—s shown the

possi˜ility of h—nd movements re™ognition through the ™l—ssi(™—tion of these neuroE

mus™ul—r iwq sign—lsF xowD in this se™ond p—rt of thesisD — new study will ˜e iniE

ti—tedF „his study ™on™erns the —˜ility of ˜uilded mus™uloskelet—l model to ™—pture

—nd identify the highly nonEline—r dyn—mi™sD ™—se of kneeEjoint dyn—mi™sD of hum—n

motion —s — result of FES stimul—tionsF „his system h—s ™omplex nonline—r meE

™h—ni™—l propertiesF „he —™™ur—™y of ™omputer models depends on experiment—l d—t—

me—surement —nd the power of intelligent ™omput—tion—l methodsF yur developed

fuzzyEidenti(™—tion system from experiment—l d—t— demonstr—tes the model9s —˜ility

to ™—pture the nonline—r timeEv—rying e'e™ts o˜served experiment—lly in qu—dri™eps

                                       IWI
          IWP                           VFH   wus™uloskelet—l dyn—mi™s identi(™—tion



mus™lesF „he ex—mined system ™onsisted of the qu—dri™epsD surf—™e ele™tri™—l stimuE

l—tion @piƒA sign—ls —nd — freely swinging sh—nkF „he output of the system is the

—ngul—r positionD me—sured ˜y extern—lly mounted sensorsF „he g—ol is identi(™—E

tion model of the —™tive qu—dri™eps dyn—mi™s @tot—l qu—dri™epsEsh—nk systemA —nd

the FES Eindu™ed movement @—ngle predi™tionAF sn few wordsD the t—sk is resumed in

˜uilding ™omputer model of the mus™uloskelet—l system th—t ™—n reprodu™e the musE

™uloskelet—l dyn—mi™s response of ele™tri™—l stimul—tion @FES A with good pre™isionF

hyn—mi™—l systems —re ™omplex systems like in hum—n movement fun™tions —nd other

re—l systemsF „hey —re des™ri˜ed ˜y system v—ri—˜les whose v—lues —t the next time

step ™—nnot ˜e predi™t with ™omplete ™ert—intyF fuilding models of re—l dyn—mi™—l

systems needs suit—˜le (delity to des™ri˜e —nd identify the system ™omponents —nd

their inter—™tions with the environmentF „hese models should —dequ—tely mimi™ the

dis™rete motor unit stru™ture of qu—dri™eps mus™lesF u—ntit—tive studies of mus™uE

loskelet—l dyn—mi™s m—y ˜e divided in two typesX

1) Morphological modelsX the mus™le is represented —s one single ™omponent with
vis™oel—sti™ properties ‘V“F „he wellE™ontrolled phenomenologi™—l studies of isol—ted

mus™le tissue re—lised ˜y rill is known —s hillEmodelF „his ™l—ssi™—l model ™onsists of

™ontr—™tile element @CE A —nd the series vis™oel—sti™ element @VE AF „he ™omponent

@CE A h—s no e'e™t in ™—se of mus™le extensionD its for™e is depending on the speed of

mus™le9s )exionF

„his type of model h—s — stru™ture whi™h is rel—ted to the —n—tomy —nd physiologyF

„he we—kness of this —ppro—™h de—l with the stru™ture model p—r—metersD whi™h is

uniqueF

2) Models of adaptable parametersX su™h models —re ˜uilded on the ˜—sis of
VFPF pound—tions —nd wethods                                              IWQ



over—ll system ˜eh—vior ‘QR“ —nd —re derived from me—sured inputEoutput d—t— setsF

„hese models ™—n des™ri˜e —nd identify qu—ntit—tive ˜eh—viors of this re—l system9s

dyn—mi™s @kneeEjoint dyn—mi™sA through the —n—lysis of the rel—tion ˜etween me—E

sured experiment—l inputEoutput d—t— setsF rowever €ro™ess identi(™—tion ˜—sed

upon ™onvention—l m—them—ti™—l models eFgFD line—r or nonline—r di'erenti—l equ—E

tionsD —re not well suited for de—ling with illEde(nedD ™omplex —nd un™ert—in systems

‘PS“F „his study ™onsiders this se™ond type of modelsF por this t—sk —n e0™ient fuzzy

identi(™—tion model is developed see our pu˜li™—tion ‘UP“




8.2 Foundations and Methods
„he rese—r™h in system identi(™—tion ™overs — wide —ppli™—tionsD system identi(™—tion

is the pro™edure of m—king m—them—ti™—l models of systems st—rting from experiE

ment—l d—t—D me—surementsD —nd o˜serv—tionsF „he model of — system is often very

import—nt for —n—lysisD ™ontrol designD simul—tion —nd predi™tionF rowever for the

re—l ™omplex systemsD like fiomedi™—l systems in our lifeD it9s not e—sy to (nd —lE

w—ys modelsF sn studying mus™uloskelet—l system in hum—nsD rese—r™hers must rely

on ™omprehensive m—them—ti™—l models representing the system of interest for simuE

l—ting ˜eh—viors whi™h would only ˜e experiment—lly o˜serv—˜leF „he ˜uilded models

must ˜e ™omp—ti˜le to the sign—ls )ow ˜etween the input —nd the outputF sn the

liter—ture there —re — num˜er of developed models to help the ˜uilding of mus™uE

loskelet—l dyn—mi™sF „he go—l is to use the predi™tive —˜ility of e—™h model to further

our underst—nding of how these systems workF

w—them—ti™s serves —s the l—ngu—ge with whi™h we try to underst—nd how n—ture
          IWR                           VFH   wus™uloskelet—l dyn—mi™s identi(™—tion



worksF w—ny systems —re modeled with — ™ontinuous time v—ri—˜le tF „he ™ontinuous

systems ™—n ˜e des™ri˜ed with di'erenti—l equ—tions whi™h in its simplest form looks

likeX x(t) = f (t, x)F rowever — physi™—l setting is often redu™ed to — set of dis™rete
       ´

me—surementsF sn dis™reteEsystems these me—surements —re given —t — sequen™e of

spe™i(™ timesF ƒpe™i(™ v—lues of the me—surements of the system —re often ™—lled the

st—te of this dyn—mi™—l systemD the st—te sp—™e is the unit interv—lF ‡hen — system

is qu—li(ed —s — line—r systemD it is possi˜le to use the responses of — sm—ll set of

inputs to predi™t the response to —ny possi˜le inputF „o see whether — system is

line—rD we need to test whether it o˜eys ™ert—in rules of line—r systemsF „he two ˜—si™

tests of line—rity —re homogeneity —nd —dditivity —nd ƒhiftEinv—ri—n™eF romogeneity

of — system doesn9t produ™e or ™—use response ™ompression or response exp—nsionF

wost of re—l life pro˜lems involve nonline—r systemsF rowever it is possi˜le to —pE

proxim—te — nonline—r system ˜y — line—r oneF „his is ™—lled line—ris—tion of nonline—r

systemsF „he m—in ide— of line—ris—tion is to —pproxim—te — nonline—r system ˜y —

line—r one —round the equili˜rium pointF ƒystem dyn—mi™s ™—n ™h—nge signi(™—ntly

with — ™h—nge in the system oper—ting ™onditionsF e system ™—n ˜e represented with

multiple lo™—l modelsD e—™h lo™—l model is v—lid for — spe™i(™ oper—ting regionF vo™—l

model ™—n ˜e — set of some ˜—sis —™tiv—tion fun™tionsD —s in (gure VFID in ™—se of two

dimension—l W lo™—l models using ˜—sis q—ussi—n —™tiv—tion fun™tionsF „here —re two

™omponents to identify — modelX the stru™ture —nd the p—r—metersF „he stru™ture is

the num˜er of lo™—l modelsD the ™entres of their —™tiv—tion fun™tions —nd their widthsF

„he lo™—l model9s p—r—meters ™ould ˜e the ™omplete set of ™oe0™ients for these lo™—l

modelsF

w—ny p—r—meter estim—tion —lgorithms —re —v—il—˜le to identify the p—r—meters of
VFQF ixperiment—l setup —nd pro™edure                                    IWS




   pigure VFIX „wo dimension W lo™—l models with q—ussi—n —™tiv—tion fun™tionsF


these lo™—l modelsF „he models themselves ™—n ˜e ˜l—™k ˜ox systems @neur—l netE

worksA or white ˜ox @fuzzy networksA systemsD without the need for expli™it higher

order deriv—tive fun™tion formsF „his type of models —re —ppli™—˜le in — l—rge v—riety

of ™ontextsD in™luding very ™omplex modelsF




8.3 Experimental setup and procedure
ixperiment—l me—surements —nd pro™edures —re done in w—x €l—n™k snstitute of

w—gde˜urgD qerm—nyF e short des™ription of this experiment—l pro™edureD (gure VFPD

is given using the me—surement proto™ol from this v—˜or—toryF ƒurf—™e stimul—tion

ele™trodes —re pl—™ed on the thighD the qu—dri™eps group of mus™les form the m—jor

p—rt of the mus™les on the front of the thighF „he knee —ngle θ @system outputA ˜eE

tween thigh —nd sh—nk is s—mpled —t PHrzD —nd me—sured using —n ele™trogoniometerF

snput sign—l is the v—ri—˜le pulse width of the monoEph—si™ ™urrent pulses with (xed

frequen™yD PHrzD —nd (xed emplitudeF „he r—nge of θ —ngle v—ri—tion ˜etween 90o
            IWT                         VFH   wus™uloskelet—l dyn—mi™s identi(™—tion



                            Motor      Electrical pulses
                            nerves            FES

                                                        Goniometer


                  Sensory
                  nerves



                            pigure VFPX we—surement setupF

@‚est positionA —nd 180o @full extensionAD is norm—lised to the r—nge z a ‘ HD I“F w—ny

tests —re ™—rried outD —nd ™l—ssi(ed ˜y the kind of experiments into three experiment—l

sessionsF „hese d—t— —re —lre—dy used for modelling —nd ™ontrol using neur—l networks

‘TH“ ‘SW“

   1) Test-AX the purpose of this test is to est—˜lish — suit—˜le stimul—tion ™urrent
AmplitudeD (gure VFQF „he ™urrent level I is equ—l to 40mAD —nd stimul—tion frequen™y
f is equ—l to 20HzF „his sign—l will ˜e used —s v—lid—tion sign—lF

   2) Test-SC X this is —n openEloop test sign—l where the pulseEwidth possesses
spe™i(™ Sto™h—sti™ Ch—r—™teristi™sF „he go—l is to gener—te — sequen™e of input steps

whi™h le—ds to —n —lmost uniform distri˜ution over the interv—l of the outputF ‡e

h—ve two me—surements of this this sign—l typeD testEƒgI in (gure VFR —nd tr—inEƒgP

in (gure VFSF „he (rst one will ˜e used —s testing sign—l —nd the se™ond one will ˜e

used —s tr—ining sign—lF
VFQF ixperiment—l setup —nd pro™edure                               IWU




                      pigure VFQX we—surement of Test-AF




              pigure VFRX we—surement of Test-SC1 @testing d—t—AF
        IWV                              VFH   wus™uloskelet—l dyn—mi™s identi(™—tion




               pigure VFSX we—surement of Train-SC2 @tr—ining d—t—AF


   3) Test-PRBS X „he PRBS sign—lD (gure VFTD is —pplied —round — r—nge of me—n
stimul—tion pulsewidth levelsF ƒuit—˜le stimul—tion me—n levels —reD µ a HFHRQD HDPQD

HFRHD HFSW —nd HFVPF „his sign—l will ˜e used —lso —s testing sign—lF




                      pigure VFTX we—surement of Test-PRBS1F
VFRF   worphologi™—l models                                               IWW



8.4      Morphological models
sn m—™ros™opi™ models the mus™le system is represented —s one single ™omponent with

vis™oel—sti™ properties ‘V“F rillEwodel is one of the e—rliest most popul—rly employed

mus™le modelD he —ttempts to ™—pture the for™eElengthEvelo™ity properties of the musE

™le in the w—y to ™re—te — me™h—ni™—l mus™le modelF „his ™l—ssi™—l model ™onsists of

™ontr—™tile element @CE A —nd the series vis™oel—sti™ element @VE AF „his type of model

h—s — stru™ture whi™h is rel—ted to the —n—tomy —nd physiologyF „he most ˜—si™ ˜uildE

ing ˜lo™ ™omprising — mus™le model is the ide—l spring in seri—l form with — d—mperF

e line—r spring ™re—tes — for™e proportion—l to its de)e™tionX Fk = KxD where F X

is the for™eD xX the de)exionD —nd K X the el—sti™ityF en ide—l d—mper ™re—tes — for™e

proportion—l to its vis™osityD Fb = B xD where B X is the vis™ous d—mping ™onst—ntF
                                      ˙

„he response of physiologi™—l tissues to — ™onst—nt for™e shows ˜oth of del—y time

response —nd — slower length evolutionD whi™h gr—du—lly —ppro—™hes —n —symptoti™

v—lueD (gure VFUF „he mus™leEjoint stru™ture ™—n then ˜e tre—ted —s — se™ond @or —




pigure VFUX ‚e—l illustr—tion of ˜oth del—yEtime —nd —symptoti™ length evolution of —
mus™le in response to for™e ex™it—tionF
        PHH                                 VFH     wus™uloskelet—l dyn—mi™s identi(™—tion



thirdA order systemF elthough — se™ond order line—r model ™—n ˜e m—them—ti™—lly

represented in sever—l w—ysDt he ˜—si™ equ—tion of motion for — se™ond order modelD

with l—pl—™e tr—nsfer fun™tion is given —sX

                                                  2
                                                 ωn
                              H(s) = a.                                            @VFRFIA
                                                        2
                                          s2 + 2sξωn + ωn

where aX — ™onst—ntD ξ Xd—mper f—™torD —nd ωn X proper system puls—tionF

sn other form this equ—tion ™—n ˜e formul—ted —sX

                                                     1
                              H(s) =          1          2ξ     1
                                                                                   @VFRFPA
                                       s2   aω 2n
                                                    + s aωn +   a

sn —n—logy form with line—r springD the model p—r—meters will t—ke the following v—lE

uesX

„he m—sseX M a aω12n D the vis™ous element B a aωn D —nd the el—sti™ element K a a F
                                                2ξ                               1


sf the vis™ous element B is ™onsidered ™onst—ntD this model will ˜e line—r system of

se™ond orderF

„his simple model is simul—tedF „he model presents me™h—ni™—l model of qu—dri™eps

mus™lesD th—t ™—use the extension of the kneeD —s P degrees of freedom pl—n—r m—nipE

ul—tor for the following p—r—meter v—lues —s ex—mpleX

B aRDS‘xFs/r—d“D K aQH‘x/r—d“D —nd M aIkgF

„he mus™leEmodel response of —n impulse ex™it—tion is shown in (gure VFVF ƒe™ond

order line—r systems —re widely used to represent — v—riety of dyn—mi™ systems —nd

h—ve ˜een used to represent mus™le dyn—mi™s ‘UH“ ‘IH“F „his simple —nd ˜—si™ modE

eling —ppro—™h for predi™ting stimul—ted mus™le properties provides — v—lu—˜le ˜—sis

for the interpret—tion —nd ™omp—rison of more ™omplex mus™le modelling —ppro—™hesF

por more ™omplex se™ond order nonline—r mus™le model see ‘IW“
VFSF €roposed hy˜rid fuzzy modelling —lgorithm                               PHI




pigure VFVX wus™le response to for™e ex™it—tion for se™ond order line—r model simul—ted
ex—mpleF



8.5 Proposed hybrid fuzzy modelling algorithm

wethods for d—t—Edriven fuzzy modelling —nd identi(™—tion —re of gre—t e0™ien™yF

w—ny pu˜li™—tions fo™us on hy˜rid neuroEfuzzy models without t—king in ™onsider—E

tion the notion of interpret—˜ility of the ˜uilded modelF ƒu™h models —re ˜l—™kE˜ox

models like in neur—l networksF sn this proposed hy˜rid modelling —lgorithm two

import—nt ™riteri— h—ve ˜een ™onsideredF „he (rst one is the pro˜lem of model iniE

ti—lis—tionD whi™h ™—n help usD in ™—se of good initi—lis—tionD to st—rt with — model th—t

is ™lose to the optim—l needed modelF „he se™ond one ™on™erns the le—rning methE

odsD with optim—l identi(™—tion model initi—lis—tion we don9t need — ™omplex le—rning

methods —nd the num˜er of le—rning epo™hs @time le—rningA will ˜e hugely redu™edF

„hese two ™riteri— h—s ˜een introdu™ed in this proposed hy˜rid modelling —lgorithmF

„he results using four di'erent testing d—t—D see following setion VFIHD show th—t this

proposed identi(erEmodel is —˜le to identify the re—l system using only its me—sured

inputEoutput d—t—F
          PHP                            VFH    wus™uloskelet—l dyn—mi™s identi(™—tion



„he optimis—tion of this proposed hy˜rid —lgorithm ™onsiders the mem˜ership fun™E

tions —nd the rule ™onsequen™e ™oe0™ients th—t minimise ™ert—in qu—dr—ti™ o˜je™tive

fun™tionF „hus the m—in go—l is to minimise the following sum of squ—red errors E in

equ—tion VFSFID see for more det—ils se™tion TFRFQX

                                 E=           (dn − xn )2                       @VFSFIA
                                      n=1,N

‡here dn X desired output @uneeEjoint —ngleAD xn X the proposed hy˜rid —lgorithm

outputD —nd N X num˜er of me—sured tr—ining d—t— s—mples —v—il—˜le from the re—l

systemF

„he ry˜rid elgorithm €roposed here h—s the following fun™tion—l stru™tureX

IA zero order Takagi-Sugeno @T.S.A model ‘TU“F

PA two inputs —s mentioned in se™tion VFSF

QA e—™h input is p—rtitioned with three g—ussi—n mem˜ership fun™tions @gbellmf AF

„hree mem˜ership fun™tionsX A1 D A2 D —nd A3 for the (rst input xD —nd three memE

˜ership fun™tionsX B1 D B2 D —nd B3 for the se™ond input y F „his p—rtition le—d to —

fuzzy model with W rulesF „hese rules —re des™ri˜ed in equ—tion VFSFPF

                         if x is Ai and y is Bj then z is rk .                  @VFSFPA

‡here i, j a ID PD QD —nd r a ID F F FD W @num˜er of rulesAF

„he degree of mem˜ership for e—™h input x —nd y is de(ned in equ—tion VFSFQX
                                                      1
                             µA, B (x, y) =                                     @VFSFQA
                                              1+         y)−b
                                                   ( (x, a )2c
‡here aD b —nd cX —re the premise p—r—meters th—t will ˜e upd—ted using the qr—dient

hes™ent @GD AD see se™tion TFPFQF „he (ring strength of e—™h rule is given —s — produ™t

of the mem˜ership degrees in equ—tion VFSFRX

          wm = µAi (x) · µBj (y), i, j = 1, 2, 3, and m = 1 , . . ., 9.         @VFSFRA
VFTF ‚ules ™onsequent p—r—meters initi—lis—tion using ‚€e                PHQ



„he over—ll output ™—n ˜e expressed —s line—r ™om˜in—tions of the ™onsequent p—r—mE

etersF wore pre™iselyD the output z ™—n ˜e written in equ—tion VFSFSX

                                                wm ∗ zm
                                        m=1,...,9
                                Z=                                             @VFSFSA
                                           m=1,...,9 wi




8.6 Rules consequent parameters initialisation using
         RPA
„he ‚—pid €rototyping elgorithm RPA ‘PR“ reposes on the f—™t th—t more — me—sured

point of tr—ining d—t— is ™lose to the ™ore of the mem˜ership fun™tionD more the

™on™lusion of the ™orresponding rule is ™lose to the desired output —sso™i—ted to this

me—sured pointF „he ™ore of — fuzzy mem˜ership fun™tion A is de(ned ˜y equ—tion

VFTFIX

                              NA = {x ∈ R µA (x) = 1}                          @VFTFIA

ix—mpleX

„he inputEoutput ™ouples {(xi , yi ); zi } —re ™onsideredD

where i = { 1, . ., N }D —nd N X num˜er of s—mplesF

i—™h rule h—s only one ™onsequent p—r—meter zp th—t represents the im—ge of the

input ™ouple (xp , yp ) with m—ximum inferen™eD where 1 ≤ p ≤ N F ‡ith this

method it9s possi˜le to (nd W prototypes from me—sured d—t— set for rules ™onsequent

p—r—metersF „his method gives r—pidly the initi—l solution ™lose to the desired output

—nd prevent the deriv—tiveE˜—sed optimis—tion —lgorithms getting stu™k to the lo™—l

minimumF
           PHR                                VFH   wus™uloskelet—l dyn—mi™s identi(™—tion



8.7 Hybrid algorithm steps

sn short wordD this —ppro—™h @hy˜rid —lgorithmA optimizesX

—A premise p—r—meters with qr—dient hes™ent @GD AD for more det—ils see se™tion

TFRFQF˜F

˜A ™onsequent p—r—meters with ve—st ƒqu—res istim—tors @LSE AD for more det—ils see

se™tion TFRFQF—F

pollowing steps give glo˜—l des™ription of this —lgorithmX

IA initi—lise the W rule ™on™lusions using ‚—pid €rototyping elgorithm @RPAAF

PA ™re—te the initi—l model from me—sured inputEoutput d—t— set —nd initi—lised rulesF

QA ™—l™ul—te the response Zmodel of this initi—lEmodelF

RA for e—™h me—sured d—t— p—irs {(xi , yi ), zi }, i = 1, . . . , N D me—sure the error ep

given —sX

ei = zidesired − zimodel F

SA epo™hs a I to epo™hEm—x

TA „est if this error Emodel is —™™ept—˜le or notX

UA if yesD then ixhF

VA —pply nonline—r p—r—meters optimis—tion for —ll mem˜ership fun™tions in the folE

lowing w—yX




                                ∂A(x)    2c
                                       =     · (1 − A(x)) · A1 (x)                 @VFUFIA
                                  ∂a      a
                             ∂A(x)    2c x − b 2c−1
                                    =    ·(       )    · (A1 (x))2                 @VFUFPA
                               ∂b     a        a
                             ∂A(x)           x − b 2c−1
                                   = −2c · (        )    · (A(x))2                 @VFUFQA
                              ∂c                a
VFVF wethodology                                                                PHS



where AX represents gbellmf fun™tionF

WA ™—l™ul—te the new mem˜ership fun™tion p—r—metersX

                                                               ∂ei
                          (a, b, c)next = (a, b, c)now − ρ                            @VFUFRA
                                                             ∂(a, b, c)

IHA —pply line—r p—r—meters optimis—tion for —ll rule ™onsequents @see se™tion TFRFQF—

IIA ™—l™ul—te the new rule ™onsequents

IPA go to step QF



8.8 Methodology
e wide ™l—ss of nonline—r dyn—mi™ pro™esses —re SISOF sn this ™—seD the kneeEjoint

dyn—mi™ pro™ess h—s one input u @pulse widthA —nd one output y @—ngleAY the dyn—mi™

model ™—n ˜e des™ri˜ed ˜y the following formul—D using T histori™—l @p—stA inputsX

u(k − 1), . . ., u(k − 6)D —nd R histori™—l outputsX y(k − 1), . . ., y(k − 4)D equ—tion

VFVFIX


   y(k) = f [u(k − 1), u(k − 2), ..., u(k − 6), y(k − 1), y(k − 2), ..., y(k − 4)].   @VFVFIA


‡here f is the fun™tion to ˜e identi(ed ˜—sed on me—surement inputEoutput d—t— of

re—l systemF „his fun™tion h—s ten @IHA inputsF „he num˜er of inputs is ˜ig to use

fuzzy modelling pro™edureF por fuzzy modelD the num˜er of rules will ˜e hugely ˜igF

sf —ll ™om˜in—tions —re ™onsidered for — fuzzy inferen™e system with IH inputsD e—™h

one with three mem˜ership fun™tionsD the grid p—rtitioning le—ds to 310 rulesD whi™h is

very l—rge for —ny pr—™ti™—l le—rning methodsF „herefor the num˜er of inputs must ˜e

redu™edD we ™onsider therefor only two inputsF „he question now is to de(ne or (nd

these two ˜est inputs ˜etween these ten inputsD whi™h ™—n give the ˜est des™ription
          PHT                            VFH   wus™uloskelet—l dyn—mi™s identi(™—tion



of our re—l system dyn—mi™sF „he solution is to ˜uild models of two inputs through

the ™om˜in—tion ˜etween histori™—l inputs —nd histori™—l outputsF „he num˜er of

™om˜in—tions is equ—l to 6 × 4 = 24F „he optimis—tion of these PR models will ˜e

done during only one epo™hD —nd then the ˜est one undergo further re(ne optimis—tion

epo™hsF

ell these PR p—irEinputs will ˜e tested in one ˜uilt modelF „his methodD se™tion

VFSD uses ™onst—nt ™onsequent p—r—meters with zeroEorder „FƒF model —nd is ˜—sed on

gener—ting only one fuzzy model @ry˜rid elgorithmA th—t employs —ll PR possi˜le d—t—

p—ir inputsF xote th—t the fuzzy model h—s nine rulesD three gener—lized ˜ellEsh—ped

mem˜ership fun™tions for e—™h inputF „he tr—ining pro™edure for e—™h p—ir input is

done during only one epo™hF

„he p—ir inputsD y(k-1) —nd u(k-6)D h—s ˜een found —s the ˜est modelD hen™e we t—ke

this p—ir —s input v—ri—˜les for the further study in following se™tion VFWF xote th—t

the ™omput—tion time for this identi(™—tion of the ˜est p—ir input is done during

PFPTTH se™ ‘AMD Athlon (tm) Processor “F „hus the ˜est found model of kneeEjoints

dyn—mi™s is des™ri˜ed ˜y the following formul—D equ—tion VFVFPX




                          yi (k) = f [ui (k − 6), yi (k − 1)].                 @VFVFPA




where i is the r—nk of the set inputD i = {1, ., ., ., N }D —nd N X num˜er of tr—ining

d—t— s—mplesF
VFWF yptimis—tion of sele™ted model                                       PHU



8.9 Optimisation of selected model
„he tr—ining d—t— set @data-sc2 AD see (gure VFS ™ont—ins VWS points @s—mplesAF i—™h

input is p—rtitioned into three fuzzy sets using gbellmf mem˜ership fun™tionsF pollowE

ing (gure VFW shows us the resulting initi—l mem˜ership fun™tionsF „he initi—l hy˜rid




pigure VFWX sniti—l mem˜ership fun™tions with overl—p equ—l to HFSD for inputI —nd
inputPF


—lgorithm is ˜uilt using des™ri˜ed r—pid prototyping methodD see se™tion VFTD with seE

le™ted p—ir inputs y(k-1) —nd u(k-6)F ‡ithout —ny optimis—tionD this initi—l model is

tested using the s—me input sign—l for tr—ining d—t— @data-sc2 AF „he output response

of this initi—l modelD is shown in (gure VFIHF „his output sign—l of our initi—l modelD

using only r—pid prototyping —lgorithmD is ™lose enough to the desired output of re—l

systemF xow this initi—l model is tr—ined during only IH epo™hsD with le—rning r—te

(xed to HFHHQ for —ll epo™hsF „he (n—l fuzzy sets gener—ted ˜y this optimised hy˜rid

model is illustr—ted in the following (gure VFII@˜AF „he time needed for the optiE

mis—tion of this hy˜rid model during IH epo™hs is equ—l to IFUTTH se™ ‘AMD Athlon

(tm) Processor “F sn this —ppli™—tion the ™onsequent p—r—meters —re rem—ined in the
        PHV                             VFH   wus™uloskelet—l dyn—mi™s identi(™—tion




pigure VFIHX ‚esponse of initi—l proposed hy˜rid model @solid lineAD —nd desired system
output @d—shed lineAF

envelope of possi˜le v—lues of re—l system outputF „he initi—l v—lues of ™onsequent

p—r—meters found with PRA —lgorithm —reX z1, z2, . . . z9 a

[0.2692 0.2159 0.3779 0.4466 0.4769 0.4686 0.6567 0.6925 0.6932]F

„he resulting v—lues —fter IH epo™hs optimis—tion —reX

[0.2238 0.2134 0.1459 0.4327 0.4787 0.5144 0.7142 0.6920 0.7139]F

prom the viewpoint of interpret—˜ilityD the ™onsequent p—r—meters h—ve physi™—l interE

pret—tion th—t represent the norm—lised —ngle ˜etween thigh —nd sh—nkD (gure VFII@™AF

„he mem˜ership fun™tions th—t p—rtition the two input sp—™e h—ve not undergos gre—t

™h—ngesD VFII@—AF




8.10 Hybrid model validation
wodel v—lid—tion is the he—rt of the identi(™—tion pro˜lemF „he following sign—ls Test-

sc1D Test-sc3D Test-a —nd Test-prbs des™ri˜ed in se™tion VFQ will ˜e tested with this

optimised hy˜rid model to ev—lu—te the qu—lities of the o˜t—ined kneeEjoint dyn—mi™s
VFIHF ry˜rid model v—lid—tion                                            PHW




pigure VFIIX —F yptimised gbellmf Y ˜F €redi™tion perform—n™e of hy˜rid elgorithm
@solid lineAD —nd system output @d—shed lineAY ™F ivolution of rules ™onsequentsY dF
irror ˜etween desired system output —nd hy˜rid model output —fter IH epo™hs @using
tr—inEd—t— set @test-sc2 AF


identi(erEmodelF

„he e0™ien™y of the this hy˜rid fuzzy modelD representing nonEline—r inputEoutput

dyn—mi™sD depends on the initi—l fuzzy p—rtition of the input sp—™eF „he tuning of the

premise fuzzy sets —nd ™onsequent p—r—meters is —™hieved through three te™hniquesX

‚—pid €rototyping elgorithmD qr—dient hes™ent —nd ve—st squ—res istim—torF




8.10.1 Signal Test-SC1
„he identi(™—tion e0™ien™y of the this hy˜rid fuzzy model representing nonEline—r

inputEoutput dyn—mi™s with d—t— test − sc1 is shown in (gure VFIPF
        PIH                            VFH   wus™uloskelet—l dyn—mi™s identi(™—tion




pigure VFIPX e˜oveX dyn—mi™ system response with hy˜rid —lgorithm @solid lineA —nd
system output @d—shed lineAF felowX the identi(™—tion error of their di'eren™eF @for
testing d—t—X test-sc1 AF


8.10.2 Signal Test-A
„he identi(™—tion e0™ien™y of the this hy˜rid fuzzy model representing nonEline—r

inputEoutput dyn—mi™s with d—t— test-A is shown in (gure VFIQF




pigure VFIQX e˜oveX dyn—mi™ system response with hy˜rid —lgorithm @solid lineA —nd
system output @d—shed lineAF felowX the error of their di'eren™eF @for testing d—t—X
test-AAF
VFIIF gon™lusion                                                        PII



8.10.3 Signal Test-PRBS
„he identi(™—tion e0™ien™y of the this hy˜rid fuzzy model representing nonEline—r

inputEoutput dyn—mi™s with d—t— test-prbs is shown in (gure VFIRF




pigure VFIRX e˜oveX dyn—mi™ system response with hy˜rid —lgorithm @solid lineA —nd
system output @d—shed lineAF felowX the error of their di'eren™eF @for testing d—t—X
test-prbs AF




8.11 Conclusion
sn this gh—pterD —n e'e™tive fuzzy identi(erEmodel ˜—sed on ry˜rid elgorithm is

proposedF sn this proposed elgorithm the fuzzy ruleE™on™lusion —nd mem˜ershipE

fun™tion p—r—meters ™—n ˜e gener—ted —nd optimized —utom—ti™—lly from the tr—ining

d—t—F

„he proposed fuzzy hy˜rid —lgorithm provides — f—st —nd e'e™tive method for identiE

(™—tion of kneeEjoint system dyn—mi™s @thighEsh—nkAF „his method fo™uses on model

simpli™ity —nd timeE™onsumingD under — s—tisf—™tory modeling —™™ur—™y with tr—nsE

p—rent fuzzy setsF „he results o˜t—ined demonstr—te th—t this hy˜rid —lgorithm —pE

pro—™h is e'e™tive for identi(™—tion of nonline—r dyn—mi™ pro™ess —nd ™—n ˜e — good
        PIP                            VFH   wus™uloskelet—l dyn—mi™s identi(™—tion



—ltern—tive when — m—them—ti™—l model of the pl—nt is not —v—il—˜leF „he further imE

provement in the model stru™tureD @for ex—mpleX three inputs —nd —d—pting le—rning

r—teAD for this method would ˜e ˜ene(™i—lF
Chapter 9
Conclusions and future works

9.1 Recapitulation
„he hum—n neuromus™uloskelet—l system is ™onsidered in this thesis in two p—rtsX IA

ƒurf—™e ele™tromyogr—m @iwqA neuromus™ul—r sign—ls re™ognition for h—nd moveE

ments ™l—ssi(™—tionF PA wus™uloskelet—l system dyn—mi™s identi(™—tionF

„he (rst go—l of this thesisD ™on™erned the ™l—ssi(™—tion of surf—™e iwq neuromus™ul—r

sign—lsD whi™h ™—n ˜e designed for the ™ontrol of myoEprostheses —nd —lso exoskeleton

devi™esF „he surf—™e ele™trodes tr—nsdu™e the motor unit —™tion potenti—ls w…e€s

into result—nt ele™tri™—l iwq sign—lD whi™h ™—n ˜e re™orded following —ppropri—te

pro™essingD —mpli(™—tion —nd (ltering pro™eduresF

iwq sign—ls —re ele™tri™—l —™tivities origin—ting in the ˜r—in —nd th—t —re tr—nsported

vi— nerve ™ells to the mus™lesF „hese sign—ls ™—use the ™ontr—™tion of mus™lesF „hese

me—surements of iwq sign—ls issued from mus™le ™ontr—™tions —re re—lis—tions of

— ™omplex timeEv—ri—nt pro™ess th—t ™ontrol ele™tri™—l —™tiv—tion of mus™lesF „hey

provide —n —™™ess to physiologi™—l pro™essesD whi™h ™—use mus™les to gener—te for™esD

produ™e movementsD —nd —™™omplish fun™tions th—t —llow the hum—n to inter—™t with

                                         PIQ
        PIR                                        WFH   gon™lusions —nd future works



the world —roundF sn the —mpli(™—tion pro™ess of these sm—ll ˜ioele™tri™ sign—lsD whi™h

—re typi™—lly in uV D it9s ne™ess—ry to redu™e —s mu™h —s possi˜le the e'e™t of noisy

ele™tri™—l sign—lsF „his sign—l @iwqA should ˜e re™orded with — ™ert—in (delity to

—ssure the tr—nsmission of its inside inform—tion @without loss of inform—tionAD whi™h

should ˜e re™ognised —nd ™l—ssi(ed —fter th—tF

sn m—ny ™—sesD the sequenti—lly lo™—lis—tions of the inform—tion ™—rried ˜y the o˜E

served sign—l —nd the distur˜—n™es —re known —s a prioriF „he o˜je™tive is then to

˜uild — new sign—l st—rting from the r—w sign—lD whi™h preserves import—nt inform—E

tion ™—rried ˜y the sign—lD —nd ex™ludes the distur˜—n™esF „he prin™iple fun™tion of

— (lter thenD is to (lter out the unw—nted p—rts of —n input sign—lF „hese unw—nted

frequen™y p—rts ™—nnot ˜e —ll elimin—tedD ˜ut only redu™edF „he MATLAB sign—l

pro™essing tool˜ox ™ont—ins — num˜er of di'erent fun™tions —nd ™omm—nds for deE

signing lowEp—ssD highEp—ss —nd ˜—ndEp—ss (ltersF higit—l (lters —re designed through

v—rious prototypesX ChebyshevD ButterworthD —nd Elliptic for IIR typeF EquirippleD

least squaresD —nd Kaiser window —re designed for FIR typeF „he optim—l type (lE

ters —re ™hosen on the ˜—sis of implement—tion ™omplexityD m—gnitude response —nd

e0™ien™yF „he design spe™i(™—tions of the ˜—ndEp—ss (lter —nd its order —re given

for m—ny ex—mplesF e ™omp—rison of these (lters w—s —ttempted in order to ev—lu—te

the —dv—nt—ges —nd dr—w˜—™ks of e—™h (lterF st w—s ™on™luded th—t IIR (lters —re

less ™omplex —nd le—d to the s—me —™™ur—™y ™l—ssi(™—tion results th—n FIR (ltersF

pilter p—ssE˜—nds h—ve — gre—t import—n™e to tr—nsmit wellEde(ned inform—tionD —nd

to reje™t other distur˜—n™esF e˜out the ™hoi™e of this (lter p—ssE˜—ndD it w—s proved

th—t one (xed p—ssE˜—nd (lter ™—n not ˜e gener—lisedD —s —n optim—l frequen™y ˜—ndD

for —ll other fe—turesF sn this thesis three di'erent —n—lysis methods —re usedX
WFIF ‚e™—pitul—tion                                                       PIS



IA timeEdom—inD PA frequen™yEdom—in —nd QA timeEfrequen™yEdom—inF „he go—l w—s to

extr—™t fe—tures ™orresponding to e—™h —n—lysis method —nd ™omp—re ˜etween themF

efter iwq sign—l preEpro™essing oper—tionD using spe™trum —n—lysis ˜—sed on shortE

time pourier tr—nsform @STFT AD whi™h is — form of lo™—l pourier —n—lysis th—t tre—ts

time —nd frequen™y simult—neouslyF st w—s possi˜le to exploit —nd to qu—ntify the

˜eh—viour of dyn—mi™ inform—tion present in these iwq sign—ls —nd design ™h—r—™E

teristi™ ve™tors @fe—turesAF ƒome of these ™h—r—™teristi™ ve™tors ™ould perform — good

dis™rimin—tion of di'erent h—nd movement ™l—ssesF

„he following t—sk w—s to redu™e the sp—™e of the num˜er of extr—™ted fe—ture ve™E

torsF PCA is — w—y of expressing — high dimension—l d—t— set in —n —ltern—tive set of

— low dimension—l d—t— set with high v—ri—˜ilityF ƒu™h method is —lso used for d—t—

visu—lis—tion —nd ™lusteringF sn this study — line—r dimension redu™tion te™hnique

@PCAA w—s investig—tedF sn this thesis it w—s shown th—t the fe—ture Fstd —loneD in

Ph fe—ture sp—™eD gives ˜y it self —n —ver—ge num˜er of mis™l—ssi(ed inst—n™es less

th—n in the ™—se of Ph redu™ed fe—ture sp—™e using PCAF ren™e we ™ould ™on™lude

th—t the sp—ti—l redu™tionD using PCAD of m—ny fe—tures for ™l—ssi(™—tion —™™ur—™y

doesn9t le—d ne™ess—rily to ˜etter resultsF

„he ™l—ssi(™—tion pro™edure is performed on the ˜—sis of ™l—sses9 fe—ture distri˜utionF

„hese ™l—ssi(™—tion models ˜elong to two ™—tegoriesF pirst —re supervised modelsD like

wultiEv—yer €er™eptronD ‚—di—l f—sis xetworksD —nd ve—rning †e™tor u—ntiz—tion

networkF ƒe™ond —re unsupervised modelsD like ƒelf yrg—nizing w—pD puzzy ƒu˜tr—™E

tive glustering —nd gompetitive v—yerF pour intelligent ™omput—tion—l —lgorithms

were ˜e used to perform the ™l—ssi(™—tion of four di'erent h—nd movements —™™ording

to their ™orresponding iwq sign—lsF sntelligent ™omput—tion—l —lgorithms used in
        PIT                                         WFH   gon™lusions —nd future works



this thesis —re wultiEv—yer €er™eptron @MLP AD ‚—di—l f—sis xetworks @RBF AD ve—rnE

ing †e™tor u—ntiz—tion network @LVQ A —nd fuzzy su˜tr—™tive ™lustering @FSC AF „he

purpose of this study w—s to illustr—te these v—rious intelligent ™omput—tion—l —lE

gorithms —nd to ™omp—re them with the perform—n™e of our proposed FTMC fuzzy

™l—ssi(erE—lgorithmF „he str—tegy of ™hoosing ˜etween di'erent ™l—ssi(™—tion methods

is of gre—t import—n™eF sn ™—se of onEline prosthesis ™ontrolD or exoskeleton devi™e ™onE

trolD the needed time for sign—l —™quisitionD then for pro™essing —nd (n—lly de™ision

™ontrolD should ˜e shortF ren™e the ™hoi™e of ™l—ssi(™—tion method should ™onsidE

ers ˜oth time ™onsuming —nd perform—n™eF por these ™onsider—tions proposed fuzzy

FTMC ™l—ssi(erE—lgorithm presents —™™ept—˜le resultsF sts —dv—nt—ge ™—n ˜e seen in

optimis—tion methodsD whi™h —re simple —nd not time ™onsumingD like qr—dient heE

s™ent @GD A —nd ve—st ƒqu—red irror @LSE AD —nd —lso utilis—tion of simple „rimmed

we—n method for determin—tion of initi—l input fuzzy sets @stru™tur—l optimis—tionAF

sn ™—se of dyn—mi™—l ™omplex systemsD like fore—rm iwq sign—ls —n—lysisD intelliE

gent ™omput—tion—l methods —re shownD through the ™omp—rison ˜etween themD their

e0™ien™y —nd —˜ility to de—l with these systems —nd to give good ™l—ssi(™—tionEmodelsF




   efter iwq neuromus™ul—r sign—ls ™l—ssi(™—tionD the se™ond p—rt of this thesisD

™onsidered the study of mus™uloskelet—l system dyn—mi™s identi(™—tionF ƒu™h identiE

(™—tion oper—tion should ˜e —˜le to ™—pture the highly nonEline—r dyn—mi™s of mus™uE

loskelet—l systems @™—se of kneeEjoint dyn—mi™sA —s — result of FES stimul—tionsF yur

developed fuzzyEidenti(er modelD from experiment—l d—t—D demonstr—ted the model9s

—˜ility to ™—pture the nonline—r timeEv—rying dyn—mi™s o˜served experiment—lly from

d—t—Eme—sureF „he ex—mined re—l system is ™onsisted of the qu—dri™epsD ƒurf—™e
WFPF ‡h—t —re the —ppli™—tions of this „hesis                              PIU



ile™tri™—l ƒtimul—tion sign—l —nd — freely swinging sh—nkF „he output of this sysE

tem is the —ngul—r positionD me—sured ˜y extern—lly mounted sensorsF „he g—ol w—s

the identi(™—tion of the dyn—mi™ rel—tionship ˜etween qu—dri™eps dyn—mi™s @tot—l

qu—dri™epsEsh—nk systemA —nd the FES Eindu™ed movement @—ngleAF ƒurf—™e stimul—E

tion ele™trodes —re pl—™ed on the qu—dri™eps group of mus™les form the m—jor p—rt of

the mus™les on the front of the thighF „he knee —ngle θ @system outputA ˜etween thigh

—nd sh—nk is s—mpled —t 20HzD —nd me—sured using —n ele™trogoniometerF snput sign—l

is the v—ri—˜le pulse width of the monoEph—si™ ™urrent pulses with (xed frequen™yD

20HzD —nd (xed emplitudeF „he r—nge of θ —ngle v—ri—tion ˜etween 90 @rest posiE

tionA —nd 180 @full extensionAD is norm—lised to the r—nge z a ‘HD I“F w—ny tests —re

™—rried outD —nd ™l—ssi(ed ˜y the kind of experiments into four experiment—l sessionsF

yne me—sured d—t— is used for this proposed model —s tr—ining @le—rningAd—t—D —nd

four other me—sured d—t— —re served for this proposed model —s ev—lu—ting @testingA

d—t—F „he proposed hy˜rid fuzzy model provided — f—st —nd e'e™tive —lgorithm for

modeling the kneeEjoint dyn—mi™s systemF „his —lgorithm is ˜—sed on model simpli™E

ity —nd timeE™omputing e0™ien™yD under — s—tisf—™tory identi(™—tion —™™ur—™y with

tr—nsp—rent fuzzy setsF



9.2 What are the applications of this Thesis
en underst—nding of iwq neuromus™ul—r sign—ls —nd mus™uloskelet—l system dyn—mE

i™s ™—n help dis—˜led persons in reg—ining lost fun™tion —nd improving their —™tivity

of d—ily living life —nd —lso for —ssessing reh—˜ilit—tion progressF woreover it en—˜les

˜etter —ssessment —nd ther—peuti™ oper—tions for themF

„he results o˜t—ined were very wellF ‡ith the known ƒhort „ime pourier „r—nsform
        PIV                                         WFH   gon™lusions —nd future works



@STFT A —nd our proposed interpret—˜le fuzzy ™l—ssi(erEmodel @FTMC A —nd —lso other

known methodsD we ™ould re—™h good —™™ur—™y ™l—ssi(™—tionsF sn ™—se of optimised

v—lues of these two p—r—metersD whi™h —reX PST ms for sign—l length —nd Pkrz for

s—mpling frequen™yD the ™l—ssi(™—tion —™™ur—™yD using our proposed —lgorithmD ™ould

r—e™h WS% see (gure UFIQF woreoverD in this thesisD it is shown th—t with only two

™h—nnels @one fe—ture ve™torA it w—s possi˜le to re™ognise —nd ™l—ssify h—nd —nd —lso

(nger )exion movementsD whi™h —re thum˜ED pointerE —nd middleE(ngerF „his dis™rimE

in—tion ™—n ˜e in™re—sed if the num˜er of ™h—nnels —nd fe—ture ve™tors —re in™re—sedF

„his is —n import—nt result th—t will determine the future implement—tions of h—ndE

prostheses ™ontrolF

„he results of (rst p—rt of this thesis ™—n ˜e —pplied to help the p—tientD with —mE

put—ted h—ndD to keep the neuromus™ul—r —™tivity of his fore—rm mus™les for the

m—nipul—tion of — myoEprosthesis or h—ndEexoskeleton devi™eF woreover this re™ogniE

tion of iwq sign—ls help to keep —lso the virtu—l neur—l —™tivity of the ˜r—in rel—ted to

fore—rmEneuromus™ul—r —™tivityF „he devi™esD myoEprosthesis —nd h—ndEexoskeletonD

™—n ˜e ™onsidered —s hum—nEm—™hine interf—™es th—t ™—n ˜e —˜le to re™ognise the deE

sired h—nd —nd (nger movements of the oper—tor —nd reprodu™e the s—me movement

—s intelligent —nd re—lEtime hum—nEm—™hine interf—™eF




   pun™tion—l ele™tri™—l stimul—tion @FES A impulses ™—n ˜e used to —™tiv—te mus™les

dis—˜led ˜y spin—l ™ord injuriesD —fter strokeD —nd support the we—k volunt—ry mus™le

—™tivitiesF „he e0™ien™y of mus™leEstimul—tor worn on the leg or —rm of p—tient —nd

pl—™ed over —'e™ted mus™les need — mus™uloskelet—l system modelsD whi™h —re —˜le to

reprodu™e the kneeEjoint dyn—mi™s or el˜owEjoint dyn—mi™sF ƒu™h systems ™—n ™ontrol
WFQF „he go—l of this rese—r™h —nd future works                           PIW



pun™tion—l ile™tri™—l ƒtimul—tion @FES A th—t will support the p—tients to —™™omplish

— right legs or —rms movementsF „he proposed interpret—˜le fuzzy hy˜rid identi(erE

model h—d — well resultsD it ™ould reprodu™e the kneeEjoint dyn—mi™s in estim—ting

of the —ngle output of four di'erent sto™h—sti™ FES sign—l inputsX (gures VFIPD VFIQD

—nd VFIR




9.3 The goal of this research and future works
„he go—l of this thesis w—s to ™l—ssify the iwq neuromus™ul—r ™ontrol sign—ls for h—nd

—nd (nger movements —nd —lso to identify the mus™uloskelet—l system of kneeEjoint

dyn—mi™s using ele™tro stimul—tion @FES AD whi™h is done with su™™essF

„he future work is —ttempted to ™om˜ine the re™ognition of iwq sign—ls —nd the

models of mus™uloskelet—l system dyn—mi™s of el˜owEjoint —nd kneeEjoint movements

‘TP“F ƒu™h models —llow determin—tion of the set of ele™tri™—l stimul—tion th—t produ™e

the desired movement through their inverse dyn—mi™ modelsF st will ˜e ne™ess—ry to

develop the ™—us—l rel—tionship ˜etween neuromus™ul—r iwq p—tterns —nd mus™uE

loskelet—l system dyn—mi™sF

fy postEstroke su˜je™tsD there —re we—k iwq sign—lsD whi™h —re extremely sm—ll —nd

un—˜le to ™ontrol the mus™lesF „he ™orre™tion ™ontrol of mus™le —™tiv—tions with ™onE

sider—tion of their mus™uloskelet—l system dyn—mi™s would ™orre™t their g—it p—ttern

so th—t they m—t™h the he—lthy g—it p—tternsF „his is — method of ™ognitive reEle—rning

to reh—˜ilit—te the mus™les of p—r—lyzed legs or —rmsD whi™h ™—nnot ˜e done with ele™E

tri™—l stimul—tion —loneF
        PPH                                         WFH   gon™lusions —nd future works



pin—lly we ™—n ™on™lude th—t this thesis ™overed the study of m—ny intelligent ™omE

put—tion—l tools th—t —re used to —n—lyze —nd pro™ess ˜ioEexperiment—l d—t—F „he

te™hniques presented —re those th—t h—ve ˜een most widely —nd su™™essfully —pplied

to the —n—lysis of physiologi™—l systemsF woreover they —ddress issues su™h —s r—ndomE

nessD ™omplexityD dyn—mi™ —nd nonline—rityF sn —dditionD in this thesis it is ˜rought

together the most useful methodsD —nd su0™ient m—them—ti™—l det—ils —re provided

to en—˜le the underst—nding of these intelligent ™omput—tion—l te™hniquesF „husD this

™omplete —nd det—iled rese—r™hD in this thesisD will ˜e useful to lifeEs™ien™e investig—E

tors on sever—l levels to re—lise sever—l proje™tsD whi™h de—l with iwq ™ontrol sign—ls

—nd mus™uloskelet—l system dyn—mi™sD —nd do further investig—tions in this —re—F
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                                         PPI
        PPP                                                            fi˜liogr—phy



‘II“ eFqF forsD Robust rbf networks, design and applicationsD fook gh—pterD idsF
    ‚FtF rowlettD vF gF t—inD €hysi™—E†erl—gX reidel˜ergD ppXIPSEISQ @PHHIAF


‘IP“ wF g—rrozz—D gF ƒuppoD pF ƒe˜—sti—niD fF w—ss—D pF †e™™hiD ‚F v—zz—riniD
    wF gutkoskyD —nd €F h—rioFD The spring hand: Development of a self adaptive
    prothesis for restoring natural grasping.D eutonomous ‚o˜ots @PHHQAF


‘IQ“ ƒF ghenD gFpFxF gow—nD —nd €FwF qr—ntD Orthogonal least squares learning algo-
    rithm for radial basis function networksD siii „r—nsF on xeur—l xetworksD volXPD
    ppX QHPEQHW @IWWIAF


‘IR“ €F h—rioD gF v—s™hiD wF g—rrozz—D iF quglielmelliD qF „etiD fF w—ss—D wF e™™—D
    hF „—ddeu™™iD —nd pF veoniFD An integrated approach for the design and develop-
    ment of a grasping and manipulation system in humanoid rebotics.D s‚yƒ PHHHD
    siiiG‚ƒt sntF gonfF on sntF ‚o˜F —nd ƒysF t—p—n @PHHHAF


‘IS“ tF †—lente de ylevire—D Semantic constraints for membership function optimi-
    sationD siiiE„r—nsF ƒystemsD w—nF gy˜ernFD ptF eD volX PWD ppX IPVEIQV @t—nD
    IWWWAF


‘IT“ wF eF hen—iD pF €—lisD —nd eF egh˜i˜D Ans based modelling and control of
    nonlinear systems.D ƒystemsD w—n —nd gy˜erneti™sD PHHR siii sntern—tion—l
    gonferen™eD volXRD ppX QRQQEQRQV @y™to˜er IHEIQ PHHRAF


‘IU“ tF hevor —nd ‚F €e™kD Statistics: the exploration and analysis of dataD Qrd ed
    xew ‰ork …ƒeF


‘IV“ wF higi™™oD vF vu™—sD —nd ‰F w—tsuok—D Comparison of control strategies for
    an emg controlled orthotic exoskeleton for the handD pro™eedingsD sntF gonfF on
    ‚o˜oti™s —nd eutom—tionD w—yEtuly @PHHRAF
fi˜liogr—phy                                                             PPQ



‘IW“ tF hingD ƒeF finderEw—™leodD —nd eƒF ‡exlerD Two-step, predictive, isometric
    force model tested on data from human and rat musclesD t eppl €hysiolF †olXVSD
    pXPIUTEPIVW @IWWVAF

‘PH“ ‚F hu'D €F xol—nD wF ‚y˜—nskyD —nd wF w—lleyD Evolution in impedance at
    the electrode-skin interface of two types of surface emg electrodes during long-
    term recordingsD €ro™eedingsD ile™trophysiology —nd uinesiologyF …niversity of
    †ienn—D eustri—F @PHHPAF

‘PI“ qF wF poodyD Supervised image classication by mlp and rbf neural networks with
    and without an exhaustively dened set of classesD „—ylor 8 pr—n™isD sntern—tion—l
    tourn—l of ‚emote ƒensingD †olume PS@ISAD ppX QHWIEQIHR @eugust IHD PHHRAF

‘PP“ ƒF pujiiD hF xishik—w—D —nd rF ‰okoFD Development of a prosthetic hand using
    adaptable control method for human characteristics.D syƒ €ressD emsterd—mD
    volX SD ppXQTHEQUT @IWWVAF

‘PQ“ €ro—kis tohn qF —nd w—nol—kis himitris qFD Digital signal processing – princi-
    ples, algorithms, and applicationsD €renti™e r—llD IWWTF

‘PR“ €F ‰F qlorenne™D Algorithmes d'apprentissage pour systèmes d'inférence oueD
    idition r—rmèsD pr—n™eD IWWWF

‘PS“ w—ri—n fF qorz—l™z—ny —nd ed—m qluszekFD Neuro-fuzzy systems for rule-based
    modelling of dynamic processesD iƒs„ PHHHD IREIS ƒeptem˜er PHHHD e—™henD qerE
    m—nyF †olXIVD pXSSEVU @PHHHAF

‘PT“ fF r—nn—ford —nd ƒF vehm—nD Shorttime fourier analysis of the electromyogram:
    Fast movements and constant contractionD siii „r—ns—™tions on fiomedi™—l
    ingineeringD volF fwiEQQD ppX IIUQEIIVI @he™F IWVTAF

‘PU“ ƒF r—ykinD Neural networks: A Comprehension FundationD €renti™e r—llD IWWVF
          PPR                                                              fi˜liogr—phy



‘PV“ yF iF roll—ndD €F tF uy˜erdD ‚F „regidgoD €F f—gwellD —nd €F rF gh—ppellD Ex-
       periences with a hierarchically controlled myoelectric handD yrthopädie „e™hnikD
       ppX STTESTW @IWWTAF

‘PW“ €—rk tF —nd ƒ—nd˜erg tF‡FD Universal approximation using radial basis functions
       networkD xeur—l gomput—tionD volX QD ppX PRTEPSU @IWWIAF

‘QH“ tF iF t—™ksonD A Users' Guide to Principal ComponentsD ‡ileyEsiiiD xew ‰orkD
       PHHQF

‘QI“ tF ƒF ‚F t—ngD gF „F ƒunD —nd iF wizut—niD Neuro-fuzzy and soft computingD
       €renti™e r—llD PHHPF

‘QP“ tFEƒF‚F t—ngD Ans: Adaptive-network-based fuzzy inference systemsD siii
       „r—nsF ƒystemsD w—n 8 gy˜erneti™s PQD ppX TTSETVS @IWWQAF

‘QQ“ s—n „F tolli'eD Principal component analysisD ƒpringerD xew ‰orkD PHHPF

‘QR“ ‚F iF ue—rney —nd sF ‡F runterD System identication of human joint dynamicsD
       fiomedi™—l ingineeringF †olXIVD pXSSEVU @IWWHAF

‘QS“ pF €eterson uend—llD iF uend—ll w™gre—ryD —nd €F qeise €rov—n™eD Muskeln:
       Funktionen und testsD …‚fex —nd psƒgri‚D PHHIF

‘QT“ „F uohonenD Learning vector quantization: Technical reportD relsinki …nivF of
       „e™hFD yt—niemiF @IWVTAF

‘QU“            D Self organization and associate memoryD ƒpringerE†erl—gD vondonD Qrd
       editionD IWVWF

‘QV“            D Improved versions of learning vector quantizationD sntern—tion—l toint
       gonferen™e on xeur—l xetworksD volume ID p—ges SRSESSH @IWWHAF
fi˜liogr—phy                                                                PPS



‘QW“          D Self-organizing mapsD ƒpringer ƒeries in snform—tion ƒ™ien™esD QHD ppF
       SW–IRRF Pnd edF xew ‰orkD IWWUF

‘RH“ fF uoskoD Neural networks and fuzzy systems. a dynamical systems approach to
       machine intelligenceD €renti™e r—llD inglewood gli'sD xtD IWWPF

‘RI“ €F tF uy˜erdD yF iF roll—ndD €F rF gh—ppelD ƒF ƒmithD ‚F „regidgoiD €F tF f—gE
       wellD —nd wF ƒn—ithFD Marcus: A two degree of freedom hand prosthesis with
       hierarchical grip control.D siii „r—ns ‚eh—˜ ingD volX Q@IAD ppX UHEUT @IWWSAF

‘RP“ u—ufm—n veon—rd —nd ‚ousseeuw €eter tFD Finding groups in data. an introduc-
       tion to cluster analysisD ‡iley ƒeries in €ro˜—˜ility —nd w—them—ti™—l ƒt—tisti™sF
       epplied €ro˜—˜ility —nd ƒt—tisti™sD xew ‰orkX ‡ileyD IWWHF

‘RQ“ vF rF vindstrom —nd ‚F sF w—gnussonD Interpretation of Myoelectric Power Spec-
       tra: A Model and its ApplicationsD €ro™eedings of the siiiX „he €hysiome —nd
       fyondD volXTSGSD ppXTSQETTPF w—y @IWWUAF

‘RR“ venn—rt vjung —nd „orkel ql—dD Modeling of dynamic systemsD €renti™e r—llD
       ƒeries sn snform—tion end ƒystem ƒ™ien™esD IWWRF

‘RS“ g—rlo tF he vu™—D Surface Electromyography: Detection and RecordingD ˜y helƒys
       sn™orpor—tedF @PHHPAF

‘RT“ ‚i™h—rd qF vyonsD Understanding digital signal processingD €renti™e r—ll €„‚D
       se™ond edition w—r™h ISD PHHRF

‘RU“ ƒF wi™er—D qF †—nnozziD eF wF ƒ—˜—tiniD —nd €F h—rioD Improving detection of
       muscle activation intervalsD siii ingineering in wedi™ine —nd fiology w—g—E
       zineD volX PH@TAD ppXQVERTF @PHHIAF

‘RV“ wF wul—sD wF polgher—iterD —nd qF qiniD An emg-controlled exoskeleton for hand
       rehabilitationD pro™eedings Wth sntF gonfF on ‚eh—˜ilit—tion —nd ‚o˜oti™sD ppXQUIE
       QURD PV tuneD I tuly @PHHSAF
        PPT                                                             fi˜liogr—phy



‘RW“ hF x—u™k —nd ‚F uruseD Designing neurofuzzy systems through backpropagationD
    ‡F €edry™zD idFD puzzy wodellingX €—r—digms —nd €r—™ti™eD ppX PHQEPPVD uluwer
    foston @IWWTAF

‘SH“ yF xerr—ndD €F ‚ousselE‚—gotD hF …r˜—niD vF €ersonn—zD —nd qF hreyfusD Train-
    ing recurrent neural networks: why and how? an illustration in process modelingD
    siii „r—nsF on xeur—l xetworks volX SD ppX IUVEIVR @IWWRAF

‘SI“ fF xisim —nd ƒF uennyD Myoelectric Hand OrthosisD tourn—l of €rostheti™s —nd
    yrthoti™sD volXP@PAD ppXIRWEISRF @IWWHAF

‘SP“ ‚i™h—rd oF hud— —nd €eter iF r—rtD Pattern classication and scene analysisD
    @IWWSAF

‘SQ“ el—n †F yppenheimD ‚on—ld ‡F ƒ™h—ferD —nd tohn ‚F fu™kD Discrete-time signal
    processingD €renti™e r—llD …ƒeD IWWVF

‘SR“ ƒopho™les tF yrf—nidisD Introduction to Signal ProcessingD IWWSF

‘SS“ w—rk tF vF yrrD Introduction to radial basis function networksD gentre for ™ogniE
    tive ƒ™ien™eD …niversity of idin˜urghD ƒ™otl—nd @IWWTAF

‘ST“ qF €u™hh—mmerD The tactile slip sensor: Integration of a miniaturized sensory
    device on an myoelectric handD ‚eh—˜ilit—tion —nd rome re—lth g—reD ppXHUEIID
    in yrthopädieE„e™hnik u—rterlyD inglishD edition sF @PHHHAF

‘SU“ wF ‚eis™hlD ‚F wikutD gF €yl—tiukD —nd ƒF ƒ™hulzD Control strategies for hand
    prostheses using myoelectric patternsD Wth itt—u puzzy golloquiumD itt—uD qerE
    m—nyF @PHHIAF

‘SV“ wF €F ‚o˜insonD hF foze™D —nd gF eF w—rshm—nD Healthcare engineering and
    electromagnetic compatibilityD €ro™F s we™h i gonfF on re—lth™—re ingineerE
    ingX v—test hevelopments —nd eppli™—tionsD vondonF pp SQETID PSEPT xovem˜erF
    @PHHQAF
fi˜liogr—phy                                                             PPU



‘SW“ „F ƒ™h—uer —nd uF tF runtD Nonlinear predictive control of knee-joint angle using
    fesD €ro™eedings of the Sth ennu—l gonferen™e of the sntern—tion—l pun™tion—l
    ile™tri™—l ƒtimul—tion ƒo™iety @spiƒƒ PHHHAD ppF RPSERPVD e—l˜orgD henm—rk
    @PHHHEHTEIVAF

‘TH“ „F ƒ™h—uerD uF tF runtD wF rF pr—serD ‡F ƒtew—rtD —nd pF €revidiD Identication
    of a biomechanical system using neural networksD speg ‡orkshop on ed—pt—tion
    —nd ve—rning in gontrol —nd ƒign—l €ro™essing PHHIDƒF fitt—ntiDppF gerno˜˜ioE
    gomoD st—ly @PHHIEHVEPWAF

‘TI“ wF ƒetnesD ‚F f—˜usk—D …Fu—ym—kD —nd rF ‚F v—n x—ut— vemkeD Similarity
    measures in fuzzy rule base simplicationD siii „r—nsF ƒystFD w—nD gy˜ernF fD
    volX PV@QA ppX QUTEQVT @IWWVAF

‘TP“ i ƒh—o —nd „hom—s ƒF fu™h—n—nD Estimation of corrective changes in mus-
    cle activation patterns for post-stroke patientsD gfi‚ fiome™h—ni™s ‚ese—r™h
    ƒymposiumF @PHHSAF

‘TQ“ †on tun ƒh—oD Mathematical statisticsD ƒpringerD PHHQF

‘TR“ fF eF ƒhenoiD Introduction to digital signal processing and lter designD ‡iley
    —nd sonsD PHHSF

‘TS“ wF ƒl—™k —nd hF fer˜r—yerD A myoelectrically controlled wrist-hand orthosis
    for brachial plexus injury: A case studyD tourn—l of €rostheti™s —nd yrthoti™sD
    volFR@QAD ppFIUIEIUR @IWWPAF

‘TT“ ‰F ƒong —nd €F ‡—ngD A predictive model based on rbf neural networkD sntelligent
    ƒystems —nd gontrolD PQEPSGHVD RRTEHWVD ronoluluD r—w—iiD …ƒe @PHHRAF

‘TU“ „F „—k—gi —nd wF ƒugenoD Fuzzy identication of systems and its applications to
    modeling and controlD siii „r—nsF ƒystemsD w—nD —nd gy˜erneti™sD volX IS@IAD
    ppX IITEIQP @IWVSAF
        PPV                                                            fi˜liogr—phy



‘TV“ xF „s™hi™holdEqürm—nD RuleNet a New Knowledge-Based Articial Neural Net-
    work Model with Application Examples in RoboticsD €hFhF thesisD i„r üri™hD
    IWWTF


‘TW“ vot( eF —dehD Outline of a new approach to the analysis of complex systems
    and decision processes.D siii „r—ns—™tions on ƒystemsD w—nD —nd gy˜erneti™sD
    volXQ@IAD ppX PVERR @t—nu—ry IWUQAF


‘UH“ qFsF —h—l—k —nd ƒF€F w—D Muscle activation and contraction: constitutive rela-
    tions based directly on cross-bridge kineticsD fiome™h—ni™—l ingineeringD €u˜wed
    e˜str—™tF †olXIIPD ppX SPETP @IWWHAF


‘UI“ wF e™™—FD On the development of a cybernetic prosthetic handD €hFhF thesisD
    ƒ™uol— ƒuperiore ƒ—nt9enn—D m—rs PHHQF


‘UP“ eF egh˜i˜ —nd pF €—lisD Eective fuzzy identication method to modeling the
    input-output behavior of the knee-joint dynamicsD ‚en™ontres pr—n™ophones sur
    l— vogique ploue et ses eppli™—tionsF sƒfxXPEVSRPVETPREQD ‚éfFXTPRD ppX IWIEIWV
    @PHHQAF


‘UQ“ eF egh˜i˜D pF €—lisD —nd pF fF yuezdouD Emg-based nger movement classi-
    cation using transparent fuzzy system.D pro™eedings of the Rth ™onferen™e of the
    iurope—n ƒo™iety for fuzzy logi™ —nd te™hnologyD i…ƒpve„D „e™hni™—l …nivF of
    g—t—loni—D ppX VITEVPID UEW ƒeptem˜er @PHHSAF


‘UR“ eF egh˜i˜D pF €—lisD ‚F gF ƒ—l˜ertD —nd „F ƒ™h—uerFD Dimension reduction eect
    on emg signal identication using mlp, rbf and lvq methods in case of relevant
    features.D eutomed T ‡orkshopF ‚osto™kE‡—rnemundeD qerm—ny @PREPS w—r™h
    PHHTAF
fi˜liogr—phy                                                            PPW



‘US“ eF egh˜i˜D pr—nk €—lisD —nd pF fF yuezdouFD Emg feature evaluation using trans-
    parent fuzzy system for hand and nger movements identication.D sn sntern—E
    tion—l peder—tion for wedi™—l —nd fiologi™—l ingineering @rrsgFAX Qrd iurope—n
    medi™—l —nd ˜iologi™—l ingineering ™onferen™eD iwfigEHSF spwfi iurope—n
    ™onferen™e on ˜iomedi™—l engineering @€r—gue gze™h ‚epu˜li™ xovem˜erGPHEPSAF
    E pro™eedingsF —gre˜ X spwfiD PITWD spwfi €ro™eedings II @PHHSAF